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The large deviations theorem and ergodicity

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  • Gu, Rongbao

Abstract

In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions.

Suggested Citation

  • Gu, Rongbao, 2007. "The large deviations theorem and ergodicity," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1387-1392.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1387-1392
    DOI: 10.1016/j.chaos.2007.01.081
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    References listed on IDEAS

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    1. 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 & Wang, Yi, 2010. "The central limit theorem and ergodicity," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1180-1184, August.
    2. Li, Risong, 2012. "A note on stronger forms of sensitivity for dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 753-758.
    3. Niu, Yingxuan, 2009. "The large deviations theorem and sensitivity," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 609-614.

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