TY - JOUR

T1 - Maximizing measures for partially hyperbolic systems with compact center leaves

AU - Hertz, Rodriguez F.

AU - Hertz, Rodriguez M.A.

AU - Tahzibi, A.

AU - Ures, R.

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

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U2 - 10.1017/S0143385711000757

DO - 10.1017/S0143385711000757

M3 - Article

AN - SCOPUS:84858641170

SN - 0143-3857

VL - 32

SP - 825

EP - 839

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 2

ER -