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Strong sensitivity of systems satisfying the large deviations theorem. (English) Zbl 1332.54203
Summary: Let \(f\) be a continuous map from a compact metric space \(X\) to itself. In this paper, We introduce two concepts of upper density one sensitivity and positive lower density sensitivity, and prove that (1) if \(f\) is a topologically strongly ergodic map, then it is upper density one sensitive; (2) if \(f\) is a sensitive map satisfying the large deviations theorem, then \(f\) is positive lower density sensitive.

MSC:
54H20 Topological dynamics (MSC2010)
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