The central limit theorem and chaos |
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Authors: | Ying-xuan Niu |
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Affiliation: | (1) Department of Mathematics and Physics, Wanxi College, Lu’an, 237012, China |
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Abstract: | Let X be a compact metric space and f : X → 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. |
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Keywords: | the central limit theorem topologically ergodic sensitive dependence on initial conditions minimal equicontinuous |
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