The large deviations theorem and sensitivity

Yingxuan Niu

Chaos, Solitons & Fractals, 2009, vol. 42, issue 1, 609-614

Abstract: Let X be a compact metric space and f:X→X be a continuous map. In this paper, 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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:1:p:609-614

DOI: 10.1016/j.chaos.2009.01.036

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