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Decay of correlation implies chaos in the sense of Devaney. (English) Zbl 1060.37002
Summary: A mixing transformation \(f:M \to M\) on a manifold \(M\) is proved to be sensitively dependent on the initial value of the iteration \(f\) and topologically transitive. Furthermore, a chaotic transformation \(f\) in the sense of Devaney with some assumption is proved to be an expanding map, which implies several statistical properties in this transformation map.

MSC:
37A25 Ergodicity, mixing, rates of mixing
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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