Residual properties and almost equicontinuity

Ethan Akin*, Eli Glasner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

64 Scopus citations

Abstract

A property P of a compact dynamical system (X, f) is called a residual property if it is inherited by factors, almost one-to-one lifts and surjecttve inverse limits. Many transitivity properties are residual. Weak disjointness from all property P systems is a residual property provided P is a residual property stronger than transitivity. Here two systems are weakly disjoint when their product is transitive. Our main result says that for an almost equicontinuous system (X, f) with associated monothetic group Λ, (X, f) is weakly disjoint from all P systems iff the only P systems upon which Λ acts are trivial. We use this to prove that every monothetic group has an action which is weak mixing and topologically ergodic.

Original languageEnglish
Pages (from-to)243-286
Number of pages44
JournalJournal d'Analyse Mathematique
Volume84
DOIs
StatePublished - 2001

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