Rigidity properties for commuting automorphisms on tori and solenoids

Manfred Einsiedler, Elon Lindenstrauss

Research output: Contribution to journalArticlepeer-review

Abstract

Assuming positive entropy, we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for these actions.

Original languageAmerican English
Pages (from-to)691-736
Number of pages46
JournalErgodic Theory and Dynamical Systems
Volume42
Issue number2
DOIs
StatePublished - 8 Feb 2022

Keywords

  • entropy
  • invariant measures
  • invariant σ-algebras
  • joinings
  • measurable factors
  • solenoid automorphism
  • toral automorphisms

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics

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