Maximizing measures for partially hyperbolic systems with compact center leaves

Rodriguez F. Hertz, Rodriguez M.A. Hertz, A. Tahzibi, R. Ures

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34 Scopus citations


We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-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 are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a 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.

Original languageEnglish (US)
Pages (from-to)825-839
Number of pages15
JournalErgodic Theory and Dynamical Systems
Issue number2
StatePublished - Apr 2012

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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