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Approximation of Bernoulli measures for non-uniformly hyperbolic systems

Published online by Cambridge University Press:  11 May 2018

GANG LIAO ,
WENXIANG SUN ,
EDSON VARGAS  and
SHIROU WANG
GANG LIAO
Affiliation:
School of Mathematical Sciences, Soochow University, Suzhou 215006, China email lg@suda.edu.cn
WENXIANG SUN
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China email sunwx@math.pku.edu.cn
EDSON VARGAS
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-090, São Paulo, SP, Brazil email vargas@ime.usp.br
SHIROU WANG
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China email wangshirou@amss.ac.cn Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G2G1, Alberta, Canada email shirou@ualberta.ca
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Abstract

An invariant measure is called a Bernoulli measure if the corresponding dynamics is isomorphic to a Bernoulli shift. We prove that for $C^{1+\unicode[STIX]{x1D6FC}}$ diffeomorphisms any weak mixing hyperbolic measure could be approximated by Bernoulli measures. This also holds true for $C^{1}$ diffeomorphisms preserving a weak mixing hyperbolic measure with respect to which the Oseledets decomposition is dominated.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 1 , January 2020 , pp. 233 - 247
Copyright
© Cambridge University Press, 2018 

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