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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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