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The central limit theorem and chaos. (English) Zbl 1199.54195
Summary: Let $$X$$ be a compact metric space and $$f: X \rightarrow X$$ be a continuous map. This paper studies some relationships between stochastic and topological properties of dynamical systems. It is shown that if $$f$$ satisfies the central limit theorem, then $$f$$ is topologically ergodic and $$f$$ is sensitively dependent on initial conditions if and only if $$f$$ is neither minimal nor equicontinuous.

##### MSC:
 54H20 Topological dynamics (MSC2010) 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 60F05 Central limit and other weak theorems
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##### References:
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