A quantitative approach to transitivity and mixing

Snoha, L’ubomír and Vladimír Špitalský

Chaos, Solitons & Fractals, 2009, vol. 40, issue 2, 958-965

Abstract: We suggest new quantitative characteristics for discrete dynamical systems called degrees of transitivity, weak mixing and strong mixing. These are numbers from [0,1]. For dynamical systems on a large class of compact metric spaces we show that the system is topologically transitive if and only if its degree of transitivity equals 1 and similarly for weak mixing and strong mixing. On the other hand we construct a simple dynamical system on the unit interval with all degrees positive.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:2:p:958-965

DOI: 10.1016/j.chaos.2007.08.052

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