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The large deviations theorem and ergodic sensitivity. (English) Zbl 1258.37021
Summary: Let \((X,d)\) be a nontrivial compact metric space and \(f:X\to X\) a continuous map. In this paper, we introduce the concept of ergodic sensitivity, which is a stronger form of sensitivity. It is shown that if \(f\) is a topologically strongly ergodic map satisfying the large deviations theorem then it is ergodically sensitive. In particular, if a continuous map \(f:T\to T\) is topologically strongly ergodic, then \(f\) is cofinitely sensitive and consequently, \(f\) is ergodically sensitive whenever \(T\) is a tree.

MSC:
37B99 Topological dynamics
37A25 Ergodicity, mixing, rates of mixing
37E25 Dynamical systems involving maps of trees and graphs
60F10 Large deviations
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