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Maximizing measures for partially hyperbolic systems with compact center leaves

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Autor(es):
Rodriguez Hertz, F. ; Rodriguez Hertz, M. A. ; Tahzibi, A. ; Ures, R.
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: Ergodic Theory and Dynamical Systems; v. 32, p. 15-pg., 2012-04-01.
Resumo

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. (AU)

Processo FAPESP: 09/17136-7 - Medidas de máxima entropia para difeomorfismos parcialmente hiperbólicos
Beneficiário:Ali Tahzibi
Modalidade de apoio: Auxílio à Pesquisa - Regular