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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Maximizing measures for partially hyperbolic systems with compact center leaves

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Author(s):
Rodriguez Hertz, F. [1] ; Rodriguez Hertz, M. A. [1] ; Tahzibi, A. [2] ; Ures, R. [1]
Total Authors: 4
Affiliation:
[1] Univ Republica, IMERL Fac Ingn, Montevideo - Uruguay
[2] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Carlos, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Ergodic Theory and Dynamical Systems; v. 32, n. 2, p. 825-839, APR 2012.
Web of Science Citations: 12
Abstract

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)

FAPESP's process: 09/17136-7 - Entropy maximizing measures for partially hyperbolic diffeomorphisms
Grantee:Ali Tahzibi
Support type: Regular Research Grants