A major part of dynamical system theory studies the iteration of diffeomorphisms under various assumptions, geometric or analytic or otherwise. It is also interesting to study them collectively. In particular, , the set of diffeomorphisms of some manifold and some number , is a group. It is for instance of interest to know when it [...]
Posts Tagged ‘hyperbolicity’
T. Fisher: Diffeomorphisms with Trivial Centralizers
Posted in Dynamics, talks, tagged centralizers, genericity, group actions, hyperbolicity, smooth dynamics, smoothness on June 3, 2010 | Leave a Comment »
Discontinuity of the topological entropy for Lozi maps
Posted in Dynamics, news, papers, tagged continuity of the entropy, Dynamics, entropy, examples, hyperbolicity, Lozi maps, piecewise affine dynamics, surface dynamics on December 10, 2009 | Leave a Comment »
I have shown that, like diffeomorphisms, piecewise affine surface homeomorphisms are approximated in entropy by horseshoes, away from their singularities. It follows in particular that their topological entropy is lower-semicontinuous: a small perturbation cannot cause a macroscopic drop in entropy. The continuity of the entropy for such maps had been an open problem for some [...]
