Conference abstracts

Session B1 - Computational Dynamics

July 15, 17:30 ~ 18:00 - Room 111

The geometry of blenders in a three-dimensional Hénon-like family

Stefanie Hittmeyer

University of Auckland, New Zealand   -   stefanie.hittmeyer@auckland.ac.nz

Blenders are a geometric tool to construct complicated dynamics in diffeomorphisms of dimension at least three and vector fields of dimension at least four. They admit invariant manifolds that behave like geometric objects which have dimensions higher than expected from the manifolds themselves. We consider an explicit family of three-dimensional Hénon-like maps that exhibit blenders in a specific regime in parameter space. Using advanced numerical techniques we compute stable and unstable manifolds in this system, enabling us to show one of the first numerical pictures of the geometry of blenders. We furthermore present numerical evidence suggesting that the regime of existence of the blenders extends to a larger region in parameter space.

Joint work with Bernd Krauskopf (University of Auckland, New Zealand), Hinke Osinga (University of Auckland, New Zealand) and Katsutoshi Shinohara (Hitotsubashi University, Japan).

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