The large deviations theorem and ergodicity

Rongbao Gu

Chaos, Solitons & Fractals, 2007, vol. 34, issue 5, 1387-1392

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.

Date: 2007
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:34:y:2007:i:5:p:1387-1392

DOI: 10.1016/j.chaos.2007.01.081

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