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 [...]
Posts Tagged ‘Lozi maps’
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 »
What we (don’t) know about Lozi
Posted in Dynamics, talks, tagged bifurcations, Dynamics, Lozi maps, open problems, piecewise affine dynamics, smooth ergodic theory on June 12, 2009 | Leave a Comment »
Duncan SANDS gave a talk for the Journée Affine Par Morceaux on the dynamics of Lozi maps. These are the piecewise affine homeomorphisms of the plane of the form where . Lozi introduced them as a toy model for the Hénon map, observing numerically some kind of strange attractor for . SANDS and ISHII have [...]
