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Maximizing measures for partially hyperbolic systems with compact center leaves

RODRIGUEZ HERTZ, F. ; RODRIGUEZ HERTZ, M. A. ; TAHZIBI, A. ; URES, R.

Ergodic theory and dynamical systems, 2012-04, Vol.32 (2), p.825-839 [Periódico revisado por pares]

Cambridge, UK: Cambridge University Press

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  • Título:
    Maximizing measures for partially hyperbolic systems with compact center leaves
  • Autor: RODRIGUEZ HERTZ, F. ; RODRIGUEZ HERTZ, M. A. ; TAHZIBI, A. ; URES, R.
  • Assuntos: Accessibility ; Bernoulli Hypothesis ; Dichotomies ; Dynamical systems ; Entropy ; Exponents ; Hyperbolic systems ; Lyapunov exponents ; Mathematical analysis ; Mathematics ; Three dimensional ; Topological manifolds
  • É parte de: Ergodic theory and dynamical systems, 2012-04, Vol.32 (2), p.825-839
  • Notas: ObjectType-Article-2
    SourceType-Scholarly Journals-1
    ObjectType-Feature-1
    content type line 23
  • Descrição: 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.
  • Editor: Cambridge, UK: Cambridge University Press
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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