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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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