Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Monday, June 19, 2017 - 16:15 in V5-148

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

A talk in the 'Oberseminar Numerik' series by
Stefanie Hittmeyer from Auckland
Abstract: 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.

This talk is based on joint work with Bernd Krauskopf, Hinke Osinga and Katsutoshi Shinohara.

Within the CRC this talk is associated to the project(s): B3