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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On mixing measures for axiom A diffeomorphisms


Author: Karl Sigmund
Journal: Proc. Amer. Math. Soc. 36 (1972), 497-504
MSC: Primary 58F15; Secondary 28A65
MathSciNet review: 0309155
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Abstract: Let f be a diffeomorphism satisfying Smale's Axiom A and X an infinite basic set such that $ f\vert X$ is topologically mixing. Let M denote the space of f-invariant measures on X with the weak topology. It is shown that for a dense set of measures $ \mu $ in $ \mathcal{M}$, the system $ (X,f,\mu )$ is Bernoulli. It follows that ``in general'' the elements of $ \mathcal{M}$ are weakly mixing.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0309155-3
PII: S 0002-9939(1972)0309155-3
Keywords: Bernoulli shift, entropy, mixing measures, Markov partitions, Markov chains, quasiregular points
Article copyright: © Copyright 1972 American Mathematical Society