Mixing $C^r$ maps of the interval without maximal measure

Sylvie Ruette

Mixing $C^r$ maps of the interval without maximal measure

Dynamical Systems 2019-01-03 v1

Authors: Sylvie Ruette

Abstract

We construct a $C^r$ transformation of the interval (or the torus) which is topologically mixing but has no invariant measure of maximal entropy. Whereas the assumption of $C^{\infty}$ ensures existence of maximal measures for an interval map, it shows we cannot weaken the smoothness assumption. We also compute the local entropy of the example.

Keywords

mixing maps interval maps maximal measure invariant measure maximal entropy local entropy

Cite

@article{arxiv.1901.00325,
  title  = {Mixing $C^r$ maps of the interval without maximal measure},
  author = {Sylvie Ruette},
  journal= {arXiv preprint arXiv:1901.00325},
  year   = {2019}
}

Comments

Published in 2002. 25 pages

Related papers

View all related →