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The large deviations theorem and sensitivity

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  • Niu, Yingxuan

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.

Suggested Citation

  • Niu, Yingxuan, 2009. "The large deviations theorem and sensitivity," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 609-614.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:609-614
    DOI: 10.1016/j.chaos.2009.01.036
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    References listed on IDEAS

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    1. Gu, Rongbao, 2007. "The large deviations theorem and ergodicity," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1387-1392.
    2. Wu, Chen & Xu, Zhengjie & Lin, Wei & Ruan, Jiong, 2005. "Stochastic properties in Devaney’s chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1195-1199.
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    Cited by:

    1. Niu, Yingxuan & Su, Shoubao, 2011. "On strong ergodicity and chaoticity of systems with the asymptotic average shadowing property," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 429-432.
    2. Niu, Yingxuan & Wang, Yi, 2010. "The central limit theorem and ergodicity," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1180-1184, August.

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