Maximizing measures for partially hyperbolic systems with compact center leaves
Abstract
We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of 3-dimensional manifolds having compact center leaves: either there is a unique entropy maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0 or, there is a finite number of entropy maximizing measures, all of them with nonzero center Lyapunov exponent (at least one with negative exponent and one with positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence we obtain an open set of topologically mixing diffeomorphisms having more than one entropy maximizing measure.
Cite
@article{arxiv.1010.3372,
title = {Maximizing measures for partially hyperbolic systems with compact center leaves},
author = {F. Rodriguez Hertz and M. A. Rodriguez Hertz and A. Tahzibi and R. Ures},
journal= {arXiv preprint arXiv:1010.3372},
year = {2010}
}