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Refined scales of weak-mixing dynamical systems: typical behaviour

Part of:Spaces with richer structuresMeasure-theoretic ergodic theoryErgodic theory

Published online by Cambridge University Press:  26 June 2019

SILAS L. CARVALHOOpen the ORCID record for SILAS L. CARVALHO[Opens in a new window] and
CÉSAR R. DE OLIVEIRAOpen the ORCID record for CÉSAR R. DE OLIVEIRA[Opens in a new window]
SILAS L. CARVALHO
Affiliation:
Departamento de Matemática, UFMG, Belo Horizonte, MG, 30161-970Brazil
CÉSAR R. DE OLIVEIRA
Affiliation:
Departamento de Matemática, UFSCar, São Carlos, SP, 13560-970Brazil
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Abstract

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We study sets of measure-preserving transformations on Lebesgue spaces with continuous measures taking into account extreme scales of variations of weak mixing. It is shown that the generic dynamical behaviour depends on subsequences of time going to infinity. We also present corresponding generic sets of (probability) invariant measures with respect to topological shifts over finite alphabets and Axiom A diffeomorphisms over topologically mixing basic sets.

Keywords

scales of mixingKoopman operatorHalmos lemmaRohlin lemma

MSC classification

Primary:37A25: Ergodicity, mixing, rates of mixing
Secondary:28D05: Measure-preserving transformations54E52: Baire category, Baire spaces

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 12 , December 2020, pp. 3296 - 3309
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Copyright
© Cambridge University Press, 2019

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