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Ergodic Theory and Dynamical Systems (1)

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Refined scales of weak-mixing dynamical systems: typical behaviour
Part of
SILAS L. CARVALHO, CÉSAR R. DE OLIVEIRA
Journal:

Ergodic Theory and Dynamical Systems / Volume 40 / Issue 12 / December 2020

Published online by Cambridge University Press:

26 June 2019, pp. 3296-3309

Print publication:

December 2020
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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.