{"id":199,"date":"2024-01-29T19:15:20","date_gmt":"2024-01-29T18:15:20","guid":{"rendered":"https:\/\/www.ub.edu\/dynsys\/?page_id=199"},"modified":"2026-02-25T19:19:34","modified_gmt":"2026-02-25T18:19:34","slug":"mguardia","status":"publish","type":"page","link":"https:\/\/www.ub.edu\/dynsys\/mguardia\/","title":{"rendered":"Marcel Guardia"},"content":{"rendered":"\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<figure class=\"wp-block-image size-full is-resized has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1537\" height=\"1537\" src=\"https:\/\/www.ub.edu\/dynsys\/wp-content\/uploads\/2024\/08\/WhatsApp-Image-2024-01-30-at-09.37.03-edited.jpeg\" alt=\"\" class=\"has-border-color has-ast-global-color-5-border-color wp-image-2513\" style=\"border-width:5px;width:311px;height:auto\" srcset=\"https:\/\/www.ub.edu\/dynsys\/wp-content\/uploads\/2024\/08\/WhatsApp-Image-2024-01-30-at-09.37.03-edited.jpeg 1537w, https:\/\/www.ub.edu\/dynsys\/wp-content\/uploads\/2024\/08\/WhatsApp-Image-2024-01-30-at-09.37.03-edited-300x300.jpeg 300w, https:\/\/www.ub.edu\/dynsys\/wp-content\/uploads\/2024\/08\/WhatsApp-Image-2024-01-30-at-09.37.03-edited-1024x1024.jpeg 1024w, https:\/\/www.ub.edu\/dynsys\/wp-content\/uploads\/2024\/08\/WhatsApp-Image-2024-01-30-at-09.37.03-edited-150x150.jpeg 150w, https:\/\/www.ub.edu\/dynsys\/wp-content\/uploads\/2024\/08\/WhatsApp-Image-2024-01-30-at-09.37.03-edited-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1537px) 100vw, 1537px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-a89b3969 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-50\"><a class=\"wp-block-button__link has-medium-font-size has-custom-font-size wp-element-button\" href=\"#AboutMarcel\">About me<\/a><\/div>\n\n\n\n<div class=\"wp-block-button has-custom-width wp-block-button__width-50\"><a class=\"wp-block-button__link has-medium-font-size has-custom-font-size wp-element-button\" href=\"#ResearchMarcel\">Research<\/a><\/div>\n\n\n\n<div class=\"wp-block-button has-custom-width wp-block-button__width-50\"><a class=\"wp-block-button__link has-medium-font-size has-custom-font-size wp-element-button\" href=\"#TeachingMarcel\">Teaching<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-content-justification-right is-layout-constrained wp-container-core-column-is-layout-f1f2ed93 wp-block-column-is-layout-constrained\" style=\"flex-basis:75%\">\n<div id=\"AboutMarcel\" class=\"wp-block-group is-layout-constrained wp-container-core-group-is-layout-2deeca47 wp-block-group-is-layout-constrained\" style=\"margin-top:0px;margin-bottom:0px;padding-top:5px;padding-right:5%;padding-bottom:5px;padding-left:5%\">\n<h2 class=\"wp-block-heading\" style=\"padding-top:17px;padding-bottom:17px;font-style:normal;font-weight:300\">About me<\/h2>\n\n\n\n<p class=\"has-medium-font-size\" style=\"margin-top:0px;margin-bottom:0px\">Marcel Guardia<\/p>\n\n\n\n<p style=\"margin-top:0px;margin-bottom:0px\"><a href=\"http:\/\/www.mat.upc.edu\/ca\">Departament de Matem\u00e0tiques i Inform\u00e0tica<\/a><br><a href=\"https:\/\/web.ub.edu\/inici\">Universitat de Barcelona<\/a><br><a href=\"https:\/\/mat.ub.edu\/\">Facultat de Matem\u00e0tiques i Inform\u00e0tica<br><\/a>Gran Via de les Corts Catalanes, 585, 08007 Barcelona.<br>Office: P2 41<br><strong>guardia<\/strong>&nbsp;at&nbsp;<strong>ub<\/strong>&nbsp;dot&nbsp;<strong>edu<\/strong>.<\/p>\n\n\n\n<p style=\"margin-top:0px;margin-bottom:0px\">Since 2022, I am Professor (Catedr\u00e0tic) at UB, where I am a member of the&nbsp;<a href=\"https:\/\/www.ub.edu\/dynsys\/\">Dynamical Systems group at UB<\/a>. I am also member of the&nbsp;<a href=\"http:\/\/www.crm.cat\/\" data-type=\"link\" data-id=\"http:\/\/www.crm.cat\/\">Centre de Recerca Matem\u00e0tica<\/a>, where I am the Scientific Director of the Mar\u00eda de Maeztu award. In 2018 and 2023 I have been awarded a&nbsp;<a href=\"https:\/\/www.icrea.cat\/ca\/icrea-academia\">Distinci\u00f3 ICREA Acad\u00e8mia<\/a>.<\/p>\n\n\n\n<p style=\"margin-top:0px;margin-bottom:0px;padding-top:0px;padding-bottom:0px\">From 2018 to 2023 I held an <a href=\"https:\/\/haminstab.barcelonatech-upc.eu\/\">ERC Starting grant<\/a>.<\/p>\n<\/div>\n\n\n\n<div id=\"ResearchMarcel\" class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" style=\"font-style:normal;font-weight:300\">Research<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Selected publications<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Marcel Guardia, Jaime Paradela, <a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>A degenerate Arnold diffusion mechanism in the Restricted 3 Body Problem<br><\/strong><a href=\"https:\/\/smf.emath.fr\/index.php\/publications\/un-mecanisme-de-diffusion-darnold-degenere-dans-le-probleme-restreint-des-trois-corps\">Annales Scientifiques de l&#8217;ENS, 58(6), 1401-1478 (2025)<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2302.06973\">arXiv<\/a>.<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.google.com\/ufg.br\/otaviomarcal\/home\">Ot\u00e1vio M. L. Gomide<\/a>, Marcel Guardia, <a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a>, <a href=\"https:\/\/zengch.math.gatech.edu\/\">Chongchun Zeng<\/a><br><strong>On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting<\/strong><br><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00222-025-01327-y\">Inventiones Mathematicae, published online (2025)<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2107.14566\">arXiv<\/a>.<\/li>\n\n\n\n<li>Andrew Clarke, Jacques Fejoz, Marcel Guardia<br><strong>Why are inner planets not inclined?<\/strong><br><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10240-024-00151-z\">Publications math\u00e9matiques de l&#8217;IH\u00c9S, <a href=\"https:\/\/mathscinet-ams-org.sire.ub.edu\/mathscinet\/publications-search?query=ji%3A5730%20y%3A2025%20v%3A141\" class=\"\">141 <\/a>(<a href=\"https:\/\/mathscinet-ams-org.sire.ub.edu\/mathscinet\/publications-search?query=ji%3A5730%20y%3A2025\" class=\"\">2025<\/a>), 1\u201398.<\/a> Available at <a href=\"https:\/\/arxiv.org\/abs\/2210.11311\">arXiv<\/a>.<br><em>Quanta Magazine<\/em>: &#8216;<a href=\"https:\/\/www.quantamagazine.org\/new-math-shows-when-solar-systems-become-unstable-20230516\/\">New Proof Finds the \u2018Ultimate Instability\u2019 in a Solar System Model<\/a>&#8216;.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"https:\/\/sites.google.com\/view\/filippo-giuliani\">Filippo Giuliani<\/a><br><strong>Arnold diffusion in Hamiltonian systems on infinite lattices<\/strong><br><a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cpa.22191\">Comm. Pure Appl. Math.<strong>&nbsp;77&nbsp;<\/strong>(2024), no.&nbsp;8, 3333\u20133426<\/a>. Available at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2204.10602\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"https:\/\/sites.lsa.umich.edu\/zhani\/\">Zaher Hani<\/a>,&nbsp;<a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/ehaus\/\">Emanuele Haus<\/a>,&nbsp;<a href=\"https:\/\/people.sissa.it\/~amaspero\/\">Alberto Maspero<\/a>,&nbsp;<a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/procesi\/\">Michela Procesi<\/a><br><strong>Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation<\/strong><br><a href=\"https:\/\/ems.press\/journals\/jems\/articles\/4835664\">J. Eur. Math. Soc. (JEMS) 25 (2023), no. 4, 1497\u20131551<\/a>. Available at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1810.03694\">arXiv<\/a>.<\/li>\n\n\n\n<li><a href=\"http:\/\/www.ceremade.dauphine.fr\/~fejoz\/\">Jacques F\u00e9joz<\/a>, Marcel Guardia,&nbsp;<a href=\"https:\/\/ist.ac.at\/en\/research\/kaloshin-group\/\">Vadim Kaloshin<\/a>, Pablo Roldan<br><strong>Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem<\/strong><br><a href=\"https:\/\/www.ems-ph.org\/journals\/show_abstract.php?issn=1435-9855&amp;vol=18&amp;iss=10&amp;rank=3&amp;srch=searchterm%7Cguardia\">Journal of the European Mathematical Society, 18(10): 2315-2403 (2016)<\/a>. See the preprint version on the&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1109.2892\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, <a href=\"https:\/\/web.mat.upc.edu\/p.martin\/\">Pau Martin<\/a>,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Oscillatory motions for the restricted planar circular three body problem<\/strong><br><a href=\"http:\/\/link.springer.com\/article\/10.1007\/s00222-015-0591-y\">Inventiones Mathematicae, 203(2): 417-492 (2016)<\/a>. See the preprint version on the&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1207.6531\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"https:\/\/ist.ac.at\/en\/research\/kaloshin-group\/\">Vadim Kaloshin<\/a><br><strong>Growth of Sobolev norms in the cubic defocusing nonlinear Schr\u00f6dinger equation<\/strong><br><a href=\"http:\/\/www.ems-ph.org\/journals\/show_abstract.php?issn=1435-9855&amp;vol=17&amp;iss=1&amp;rank=3\">Journal of the European Mathematical Society, 17 (1): 71\u2013149 (2015)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/SobolevJEMS.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Preprints<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Marcel Guardia, Jaime Paradela<br><strong>Partially hyperbolic dynamics in the 3-body problem<br><\/strong>Available at <a href=\"https:\/\/arxiv.org\/abs\/2512.02133\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, Jos\u00e9 Lamas, Tere M. Seara<br><strong>Second-species dynamics in the restricted planar circular three body problem: chaos, final motions and periodic orbits<br><\/strong>Available at <a href=\"https:\/\/arxiv.org\/abs\/2512.20430\">arXiv<\/a>.<\/li>\n\n\n\n<li>Inmaculada Baldom\u00e1, <a href=\"https:\/\/www.margiralt.com\/\">Mar Giralt<\/a>, Marcel Guardia<br><strong>Coorbital homoclinic and chaotic dynamics in the Restricted 3-Body Problem<br><\/strong>Available at <a href=\"https:\/\/arxiv.org\/abs\/2312.13819\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, <a href=\"https:\/\/web.mat.upc.edu\/p.martin\/\">Pau Mart\u00edn<\/a>, Jaime Paradela, <a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Hyperbolic dynamics and oscillatory motions in the 3 Body Problem<\/strong><br>Available at <a href=\"https:\/\/arxiv.org\/abs\/2207.14351\">arXiv<\/a>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Full list of publications<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Marcel Guardia, Jaime Paradela, <a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>A degenerate Arnold diffusion mechanism in the Restricted 3 Body Problem<br><\/strong><a href=\"https:\/\/smf.emath.fr\/index.php\/publications\/un-mecanisme-de-diffusion-darnold-degenere-dans-le-probleme-restreint-des-trois-corps\">Annales Scientifiques de l&#8217;ENS, 58(6), 1401-1478 (2025)<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2302.06973\">arXiv<\/a>.<\/li>\n\n\n\n<li>Inmaculada Baldom\u00e1, Marcel Guardia, Dmitry E. Pelinovsky<br><strong>On a countable sequence of homoclinic orbits arising near a saddle-center point <br><\/strong><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00220-025-05381-8\">Comm. Math. Phys. 406 (2025), no. 9, Paper No. 215, 65 pp<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2412.01563\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, Jos\u00e9 Lamas, <a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem<\/strong><br><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00220-025-05283-9\">Comm. Math. Phys. 406 (2025), no. 5, Paper No. 106, 64 pp<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2407.17343\">arXiv<\/a>.<\/li>\n\n\n\n<li>Elisa Maria Alessi, Inmaculada Baldom\u00e1, Mar Giralt, Marcel Guardia, Alexandre Pousse<br><strong>On the role of the fast oscillations in the secular dynamics of the lunar coplanar perturbation on Galileo satellites<br><\/strong>To appear in Communications in Nonlinear Science and Numerical Simulation. Available at <a href=\"https:\/\/arxiv.org\/abs\/2405.14593\">arXiv<\/a>.<\/li>\n\n\n\n<li>Elisa Maria Alessi, Inmaculada Baldom\u00e1, Mar Giralt, Marcel Guardia<br><strong>On the Arnold diffusion mechanism in Medium Earth Orbit<\/strong><br>To appear in Journal of Nonlinear Science. Available at <a href=\"https:\/\/arxiv.org\/abs\/2403.01283\">arXiv<\/a>.<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.google.com\/ufg.br\/otaviomarcal\/home\">Ot\u00e1vio M. L. Gomide<\/a>, Marcel Guardia, <a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a>, Chongchun Zeng<br><strong>On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting<\/strong><br><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00222-025-01327-y\">Inventiones Mathematicae, <a href=\"https:\/\/mathscinet-ams-org.sire.ub.edu\/mathscinet\/publications-search?query=ji%3A5730%20y%3A2025%20v%3A141\" class=\"\">141 <\/a>(<a href=\"https:\/\/mathscinet-ams-org.sire.ub.edu\/mathscinet\/publications-search?query=ji%3A5730%20y%3A2025\" class=\"\">2025<\/a>), 1\u201398.<\/a> Available at <a href=\"https:\/\/arxiv.org\/abs\/2107.14566\">arXiv<\/a>.<\/li>\n\n\n\n<li>Andrew Clarke, Jacques Fejoz, Marcel Guardia<br><strong>Why are inner planets not inclined?<\/strong><br><a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cpa.22191\">Publications math\u00e9matiques de l&#8217;IH\u00c9S, published online (2024)<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2210.11311\">arXiv<\/a>.<\/li>\n\n\n\n<li>Inmaculada Baldom\u00e1, <a href=\"http:\/\/wms.mat.agh.edu.pl\/~mcapinsk\/home.html\">Maciej J. Capi\u0144ski<\/a>, Mar Giralt, Marcel Guardia<br><strong>Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant<\/strong><br><a href=\"http:\/\/Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant\">Discrete Contin. Dyn. Syst. 45 (2025), no. 1, 56\u201388<\/a>. Available at <a href=\"https:\/\/arxiv.org\/abs\/2312.13138\">arXiv<\/a>.<\/li>\n\n\n\n<li>Pietro Baldi, Filippo Giuliani, Marcel Guardia, Emanuele Haus<br><strong>Effective chaos for the Kirchhoff equation on tori<\/strong><br><a href=\"https:\/\/ems.press\/journals\/aihpc\/articles\/14199192\">Ann. Inst. H. Poincar\u00e9 C Anal. Non Lin\u00e9aire 42 (2025), no. 2, 281\u2013330<\/a>. Available at\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2303.00688\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"https:\/\/sites.google.com\/view\/filippo-giuliani\">Filippo Giuliani<\/a><br><strong>Arnold diffusion in Hamiltonian systems on infinite lattices<\/strong><br><a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cpa.22191\">Comm. Pure Appl. Math.<strong>&nbsp;77&nbsp;<\/strong>(2024), no.&nbsp;8, 3333\u20133426<\/a>. Available at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2204.10602\">arXiv<\/a>.<\/li>\n\n\n\n<li>Clarke, Andrew; Fejoz, Jacques; Guardia, Marcel<br><strong>A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes<\/strong><br>Arch. Ration. Mech. Anal. 248 (2024), no. 2, Paper No. 19, 73 pp.<\/li>\n\n\n\n<li>Fejoz, Jacques; Guardia, Marcel<br><strong>A remark on the onset of resonance overlap<\/strong><br>Regul. Chaotic Dyn. 28 (2023), no. 4-5, 578\u2013584.<\/li>\n\n\n\n<li>Baldom\u00e1, Inmaculada; <a href=\"https:\/\/www.margiralt.com\/\">Giralt, Mar<\/a>; Guardia, Marcel<br><strong>Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula<\/strong><br>Adv. Math. 430 (2023), Paper No. 109218, 72 pp.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"https:\/\/sites.lsa.umich.edu\/zhani\/\">Zaher Hani<\/a>,&nbsp;<a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/ehaus\/\">Emanuele Haus<\/a>,&nbsp;<a href=\"https:\/\/people.sissa.it\/~amaspero\/\">Alberto Maspero<\/a>,&nbsp;<a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/procesi\/\">Michela Procesi<\/a><br><strong>Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation<\/strong><br><a href=\"https:\/\/ems.press\/journals\/jems\/articles\/4835664\">J. Eur. Math. Soc. (JEMS) 25 (2023), no. 4, 1497\u20131551<\/a>. Available at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1810.03694\">arXiv<\/a>.<\/li>\n\n\n\n<li>Baldom\u00e1, Inmaculada; <a href=\"http:\/\/wms.mat.agh.edu.pl\/~mcapinsk\/home.html\">Capi\u0144ski, Maciej J.<\/a>; Guardia, Marcel; Seara, Tere M.<br><strong>Breakdown of heteroclinic connections in the analytic Hopf-zero singularity: rigorous computation of the Stokes constant<\/strong><br>J. Nonlinear Sci. 33 (2023), no. 2, Paper No. 28, 47 pp.<\/li>\n\n\n\n<li>Clarke, Andrew; Fejoz, Jacques; Gu\u00e0rdia, Marcel<br><strong>Topological shadowing methods in Arnold diffusion: weak torsion and multiple time scales<\/strong><br>Nonlinearity 36 (2023), no. 1, 426\u2013457.<\/li>\n\n\n\n<li>Baldom\u00e1, Inmaculada; <a href=\"https:\/\/www.margiralt.com\/\">Giralt, Mar<\/a>; Guardia, Marcel<br><strong>Breakdown of homoclinic orbits to L3 in the RPC3BP (I). Complex singularities and the inner equation<\/strong><br>Adv. Math. 408 (2022), Paper No. 108562, 64 pp.<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.google.com\/view\/filippo-giuliani\">Giuliani, Filippo<\/a>; Guardia, Marcel<br><strong>Sobolev norms explosion for the cubic NLS on irrational tori<\/strong><br>Nonlinear Anal. 220 (2022), Paper No. 112865, 25 pp.<\/li>\n\n\n\n<li><a href=\"http:\/\/wms.mat.agh.edu.pl\/~mcapinsk\/home.html\">Capi\u0144ski, Maciej J.<\/a>; Guardia, Marcel; Mart\u00edn, Pau; M-Seara, Tere; Zgliczy\u0144ski, Piotr<br><strong>Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem<\/strong><br>J. Differential Equations 320 (2022), 316\u2013370.<\/li>\n\n\n\n<li>Guardia, Marcel; Paradela, Jaime; Seara, Tere M.; Vidal, Claudio<br><strong>Symbolic dynamics in the restricted elliptic isosceles three body problem<\/strong><br>J. Differential Equations 294 (2021), 143\u2013177.<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.google.com\/view\/filippo-giuliani\">Giuliani, Filippo<\/a>; Guardia, Marcel; <a href=\"https:\/\/web.mat.upc.edu\/p.martin\/\">Martin, Pau<\/a>; Pasquali, Stefano<br><strong>Chaotic-like transfers of energy in Hamiltonian PDEs<\/strong><br>Comm. Math. Phys. 384 (2021), no. 2, 1227\u20131290.<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.google.com\/view\/filippo-giuliani\">Giuliani, Filippo<\/a>; Guardia, Marcel; <a href=\"https:\/\/web.mat.upc.edu\/p.martin\/\">Martin, Pau<\/a>; Pasquali, Stefano<br><strong>Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs<\/strong><br>Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 32 (2021), no. 1, 149\u2013166.<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.google.com\/ufg.br\/otaviomarcal\/home\">Gomide, Ot\u00e1vio M. L.<\/a>; Guardia, Marcel;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\"> Seara, Tere M.<\/a><br><strong>Critical velocity in kink-defect interaction models: rigorous results<\/strong><br>J. Differential Equations 269 (2020), no. 4, 3282\u20133346.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"https:\/\/sites.lsa.umich.edu\/zhani\/\">Zaher Hani<\/a>,&nbsp;<a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/ehaus\/\">Emanuele Haus<\/a>,&nbsp;<a href=\"https:\/\/people.sissa.it\/~amaspero\/\">Alberto Maspero<\/a>,&nbsp;<a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/procesi\/\">Michela Procesi<\/a><br><strong>A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation<\/strong><br>Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 4, 865\u2013880. Available on <a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/GHHMP_review_v2.pdf\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.terpconnect.umd.edu\/~vkaloshi\/\">Vadim Kaloshin<\/a>, Jianlu Zhang<br><strong>Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem<\/strong><br><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00205-019-01368-7\">Archive for Rational Mechanics and Analysis, 233(2): 799-836 (2019)<\/a>. See the preprint version on&nbsp;<a href=\"https:\/\/arxiv.org\/pdf\/1805.00800.pdf\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, Pau Martin, Lara Sabbagh,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Oscillatory orbits in the restricted elliptic planar three body problem<\/strong><br><a href=\"https:\/\/aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=13287\">Discrete and Continuous Dynamical Systems A, 37(1): 229-256 (2017)<\/a>. See the preprint version on&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1506.04551\">arXiv<\/a>.<\/li>\n\n\n\n<li><a href=\"http:\/\/ricerca.mat.uniroma3.it\/users\/ehaus\/\">Emanuele Haus<\/a>, Marcel Guardia,&nbsp;<a href=\"http:\/\/www1.mat.uniroma1.it\/people\/mprocesi\/\">Michela Procesi<\/a><br><strong>Growth of Sobolev norms for the analytic NLS on T2<\/strong><br><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0001870816308015\">Advances in Mathematics, 301(1): 615-692 (2016)<\/a>. See the preprint version on the&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1503.02468\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.terpconnect.umd.edu\/~vkaloshi\/\">Vadim Kaloshin<\/a>, Jianlu Zhang<br><strong>A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems<\/strong><br><a href=\"http:\/\/link.springer.com\/article\/10.1007\/s00220-016-2705-9\">Communications in Mathematical Physics, 348(1): 321-361 (2016)<\/a>. See the preprint version on the&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1503.08301\">arXiv<\/a>.<\/li>\n\n\n\n<li><a href=\"http:\/\/www.ceremade.dauphine.fr\/~fejoz\/\">Jacques F\u00e9joz<\/a>, Marcel Guardia,&nbsp;<a href=\"http:\/\/www.terpconnect.umd.edu\/~vkaloshi\/\">Vadim Kaloshin<\/a>, Pablo Roldan<br><strong>Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem<\/strong><br><a href=\"https:\/\/www.ems-ph.org\/journals\/show_abstract.php?issn=1435-9855&amp;vol=18&amp;iss=10&amp;rank=3&amp;srch=searchterm%7Cguardia\">Journal of the European Mathematical Society, 18(10): 2315-2403 (2016)<\/a>. See the preprint version on the&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1109.2892\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.ceremade.dauphine.fr\/~fejoz\/\">Jacques F\u00e9joz<\/a><br><strong>Secular instability in the spatial three-body problem<\/strong><br><a href=\"http:\/\/link.springer.com\/article\/10.1007\/s00205-015-0962-y\">Archive for Rational Mechanics and Analysis, 221(1): 335-362 (2016)<\/a>. See the preprint version on&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1505.05389\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, Pau Martin,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Oscillatory motions for the restricted planar circular three body problem<\/strong><br><a href=\"http:\/\/link.springer.com\/article\/10.1007\/s00222-015-0591-y\">Inventiones Mathematicae, 203(2): 417-492 (2016)<\/a>. See the preprint version on the&nbsp;<a href=\"http:\/\/arxiv.org\/abs\/1207.6531\">arXiv<\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.terpconnect.umd.edu\/~vkaloshi\/\">Vadim Kaloshin<\/a><br><strong>Growth of Sobolev norms in the cubic defocusing nonlinear Schr\u00f6dinger equation<\/strong><br><a href=\"http:\/\/www.ems-ph.org\/journals\/show_abstract.php?issn=1435-9855&amp;vol=17&amp;iss=1&amp;rank=3\">Journal of the European Mathematical Society, 17 (1): 71\u2013149 (2015)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/SobolevJEMS.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Marcel Guardia<br><strong>Growth of Sobolev norms in the cubic defocusing nonlinear Schr\u00f6dinger equation with a convolution potential<\/strong><br><a href=\"http:\/\/link.springer.com\/article\/10.1007%2Fs00220-014-1977-1\">Communications in Mathematical Physics, 329 (1): 405\u2013434 (2014)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/NLSConvolutionPotential.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Marcel Guardia<br><strong>Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedom<\/strong><br><a href=\"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=8150\">Discrete and Continuous Dynamical Systems A, 33 (7): 2829-2859 (2013)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/SplittingResonanciaPublished.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Inma Baldom\u00e1, Marcel Guardia, Ernest Fontich,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results<\/strong><br><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S002203961200366X\">Journal of Differential Equations, 253 (12): 3304-3439 (2012)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/SplittingGeneralArxiv.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation<\/strong><br><a href=\"http:\/\/iopscience.iop.org\/0951-7715\/25\/5\/1367\">Nonlinearity, 24 (5): 1367-1412 (2012)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/SplittingMeromorf.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a>,&nbsp;<a href=\"http:\/\/www.ime.unicamp.br\/~teixeira\/Marco\/Bem-vindos.html\">Marco Antonio Teixeria<\/a><br><strong>Generic bifurcations of low codimension of planar Filippov Systems<\/strong><br><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0022039610004456\">Journal of Differential Equations, 250 (4): 1967-2023 (2011)&nbsp;<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/GTS2011.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Marcel Guardia,&nbsp;<a href=\"http:\/\/www.enm.bris.ac.uk\/anm\/staff\/sjh.html\">S. John Hogan<\/a>,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>An analytical approach to codimension 2 sliding bifurcations in the dry friction oscillator<\/strong><br><a href=\"http:\/\/epubs.siam.org\/doi\/abs\/10.1137\/090766826\">SIAM Journal on Applied Dynamical Systems, 9: 769\u2013798 (2010)<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/090766826.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n\n\n\n<li>Marcel Guardia, Carme Oliv\u00e9,&nbsp;<a href=\"http:\/\/www.ma1.upc.edu\/personal\/mseara\">Tere M. Seara<\/a><br><strong>Exponentially small splitting for the pendulum: a classical problem revisited<\/strong><br><a href=\"http:\/\/www.springerlink.com\/content\/30043804j0453783\/\">Journal of Nonlinear Science, 20: 595-685, (2010)&nbsp;<\/a>.&nbsp;<a href=\"https:\/\/web.mat.upc.edu\/marcel.guardia\/SplittingPendulum.pdf\"><strong>[PDF]<\/strong><\/a>.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"#AboutMarcel\">Back to top<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div id=\"TeachingMarcel\" class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" style=\"font-style:normal;font-weight:300\">Teaching<\/h2>\n\n\n\n<p style=\"margin-top:0px;margin-bottom:0px\">This year I am teaching<\/p>\n\n\n\n<ul style=\"margin-top:0px;margin-bottom:0px\" class=\"wp-block-list\">\n<li>Equacions diferencials at the <em><a href=\"https:\/\/mat.ub.edu\/graumatematiques\/\">Grau de Matem\u00e0tiques<\/a><\/em>.<\/li>\n\n\n\n<li style=\"margin-top:0px;margin-bottom:0px\">Qualitative theory of ODE&#8217;s and Hamiltonian systems at the <em><a href=\"https:\/\/mat.ub.edu\/masteradvancedmathematics\/\">Master in Advanced Mathematics<\/a><\/em>.<\/li>\n<\/ul>\n\n\n\n<p style=\"margin-top:0px;margin-bottom:0px\"><\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"#AboutMarcel\">Back to top<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>About me Marcel Guardia Departament de Matem\u00e0tiques i Inform\u00e0ticaUniversitat de BarcelonaFacultat de Matem\u00e0tiques i Inform\u00e0ticaGran Via de les Corts Catalanes, 585, 08007 Barcelona.Office: P2 41guardia&nbsp;at&nbsp;ub&nbsp;dot&nbsp;edu. Since 2022, I am Professor (Catedr\u00e0tic) at UB, where I am a member of the&nbsp;Dynamical Systems group at UB. I am also member of the&nbsp;Centre de Recerca Matem\u00e0tica, where I [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":156,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"unboxed","site-sidebar-style":"boxed","ast-global-header-display":"disabled","ast-banner-title-visibility":"disabled","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"disabled","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-199","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/pages\/199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/comments?post=199"}],"version-history":[{"count":45,"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/pages\/199\/revisions"}],"predecessor-version":[{"id":3584,"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/pages\/199\/revisions\/3584"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/media\/156"}],"wp:attachment":[{"href":"https:\/\/www.ub.edu\/dynsys\/wp-json\/wp\/v2\/media?parent=199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}