Rigidity properties for commuting automorphisms on tori and solenoids

Manfred Einsiedler; Elon Lindenstrauss

doi:10.1017/etds.2021.74

Rigidity properties for commuting automorphisms on tori and solenoids

Manfred Einsiedler, Elon Lindenstrauss

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	691-736
Number of pages	46
Journal	Ergodic Theory and Dynamical Systems
Volume	42
Issue number	2
DOIs	https://doi.org/10.1017/etds.2021.74
State	Published - 8 Feb 2022

Bibliographical note

Publisher Copyright:
©

Keywords

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

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10.1017/etds.2021.74

Cite this

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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.",

keywords = "entropy, invariant measures, invariant σ-algebras, joinings, measurable factors, solenoid automorphism, toral automorphisms",

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AB - 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.

KW - entropy

KW - invariant measures

KW - invariant σ-algebras

KW - joinings

KW - measurable factors

KW - solenoid automorphism

KW - toral automorphisms

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JO - Ergodic Theory and Dynamical Systems

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IS - 2

ER -

Rigidity properties for commuting automorphisms on tori and solenoids

Abstract

Bibliographical note

Keywords

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