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Invariance principle and rigidity of high entropy measures

Tahzibi, Ali ; Yang, Jiagang

Transactions of the American Mathematical Society, 2019-01, Vol.371 (2), p.1231-1251 [Periódico revisado por pares]

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Título:
Invariance principle and rigidity of high entropy measures
Autor: Tahzibi, Ali ; Yang, Jiagang
É parte de: Transactions of the American Mathematical Society, 2019-01, Vol.371 (2), p.1231-1251
Descrição: A deep analysis of the Lyapunov exponents for stationary sequence of matrices going back to Furstenberg, for more general linear cocycles by Ledrappier, and generalized to the context of non-linear cocycles by Avila and Viana, gives an invariance principle for invariant measures with vanishing central exponents. In this paper, we give a new criterium formulated in terms of entropy for the invariance principle and, in particular, obtain a simpler proof for some of the known invariance principle results. As a byproduct, we study ergodic measures of partially hyperbolic diffeomorphisms whose center foliation is one-dimensional and forms a circle bundle. We show that for any such C^2 diffeomorphism which is accessible, weak hyperbolicity of ergodic measures of high entropy implies that the system itself is of rotation type.
Idioma: Inglês

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