Conference abstracts

Session B3 - Symbolic Analysis

July 13, 17:30 ~ 17:55 - Room B2

Non-integrability of the Armburster-Guckenheimer-Kim quartic Hamiltonian through Morales-Ramis theory

Primitivo Acosta-Humánez

Universidad Simón Bolívar, Colombia   -   primitivo.acosta@unisimonbolivar.edu.co

In this talk it will be presented the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases. Poincaré sections to illustrate the breakdown of regular motion for some parameter values. In particular we obtain conditions to get meromorphic non-integrability results through the Galoisian analysis of the variational equation of the AGK Hamiltonian which is a Legendre differential equation. On the other hand, the complete conditions for rational non-integrability results are presented through the Bostan-Combot-Safey El Din algorithm which is developed in maple.

Joint work with Martha Álvarez-Ramírez (Universidad Autónoma Metropolitana Iztapalapa, Mexico) and Teresa Stuchi (Universidade Federal do Rio de Janeiro, Brazil).

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FoCM 2017, based on a nodethirtythree design.