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The large deviations theorem and sensitivity. (English) Zbl 1198.37013
Summary: Let \(X\) be a compact metric space and \(f:X\rightarrow X\) be a continuous map. We prove that if \(f\) is a topologically strongly ergodic map, then \(f\) is sensitively dependent on initial conditions. Moreover, we investigate the relationships between the large deviations theorem and sensitivity, and show that if \(f\) satisfies the large deviations theorem, then \(f\) is sensitively dependent on initial conditions if and only if \(f\) is neither minimal nor equicontinuous.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

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