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Approximation of Bernoulli measures for non-uniformly hyperbolic systems
Published online by Cambridge University Press: 11 May 2018
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.
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- © Cambridge University Press, 2018
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