On mixing measures for axiom A diffeomorphisms
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- by Karl Sigmund PDF
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Abstract:
Let f be a diffeomorphism satisfying Smale’s Axiom A and X an infinite basic set such that $f|X$ 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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 497-504
- MSC: Primary 58F15; Secondary 28A65
- DOI: https://doi.org/10.1090/S0002-9939-1972-0309155-3
- MathSciNet review: 0309155