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Refined scales of weak-mixing dynamical systems: typical behaviour

Published online by Cambridge University Press:  26 June 2019

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

Abstract

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.

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Original Article
Copyright
© Cambridge University Press, 2019

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