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- Title
Approximation of Bernoulli measures for non-uniformly hyperbolic systems.
- Authors
LIAO, GANG; SUN, WENXIANG; VARGAS, EDSON; WANG, SHIROU
- 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.
- Publication
Ergodic Theory & Dynamical Systems, 2020, Vol 40, Issue 1, p233
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/etds.2018.33