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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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