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The large deviations theorem and ergodicity. (English) Zbl 1152.37304
Summary: Some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map $$f$$ from a compact metric space $$X$$ into itself, we show that if $$f$$ satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if $$f$$ is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions.

##### MSC:
 37B20 Notions of recurrence and recurrent behavior in dynamical systems 37A05 Dynamical aspects of measure-preserving transformations
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##### References:
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