Polynomial automorphisms of C2 with the same equilibrium measure
Romain Dujardin
Abstract
We review the following question: when do two polynomial automorphisms of C2 have the same maximal entropy measure? While the answer has been known for some time when both automorphisms are compositions of Hénon maps, the general case is more delicate. In this (mostly expository) note we explain how recent results in random dynamics give an almost complete solution to the question, and point out a number of related open problems.
Create a lesson
Related papers
Minimal acceleration and the topology of premonotonic cocycles
Xu Xia, Jiahao Xu
The Assouad Dimension of Graphs: An Affirmative Answer to Fraser's Question
Binyan Yu, Bilel Selmi, Jia Liu et al.
Multicritical pseudo-Siegel bounds and the optimality of the Brjuno condition for all neutral polynomials
Dzmitry Dudko, Yusheng Luo, Runze Zhang
Measure of Maximal Entropy for Geodesic Flows on Noncompact Manifolds of Nonpositive Curvature
Fei Liu, Xiaokai Liu
The K-property of equilibrium states for systems with non-uniform structure
Tianyu Wang
Non-convergence in heterogeneous Hegselmann-Krause dynamics: The bounded influence model
Peter Hegarty, Damiano Ognissanti, Edvin Wedin