Genericity of Infinite Entropy for Maps with Low Regularity
Dynamical Systems
2017-09-11 v1
Abstract
For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with respect to either the H\"older or the Sobolev topologies, topological entropy is generically infinite. We also prove versions of the -Closing Lemma in either of these spaces. Finally, we give examples of homeomorphisms with infinite topological entropy which are H\"older and/or Sobolev of every exponent.
Cite
@article{arxiv.1709.02431,
title = {Genericity of Infinite Entropy for Maps with Low Regularity},
author = {Edson de Faria and Peter Hazard and Charles Tresser},
journal= {arXiv preprint arXiv:1709.02431},
year = {2017}
}
Comments
51 pages, 5 figures. Comments Welcome!