Maximal entropy measures of diffeomorphisms of circle fiber bundles
Dynamical Systems
2020-11-11 v1
Abstract
We characterize the maximal entropy measures of partially hyperbolic C^2 diffeomorphisms whose center foliations form circle bundles, by means of suitable finite sets of saddle points, that we call skeletons. In the special case of 3-dimensional nilmanifolds other than the torus, this entails the following dichotomy: either the diffeomorphism is a rotation extension of an Anosov diffeomorphism -- in which case there is a unique maximal measure, with full support and zero center Lyapunov exponents -- or there exist exactly two ergodic maximal measures, both hyperbolic and whose center Lyapunov exponents have opposite signs. Moreover, the set of maximal measures varies continuously with the diffeomorphism.
Keywords
Cite
@article{arxiv.1909.00219,
title = {Maximal entropy measures of diffeomorphisms of circle fiber bundles},
author = {Raúl Ures and Marcelo Viana and Jiagang Yang},
journal= {arXiv preprint arXiv:1909.00219},
year = {2020}
}