Measurable rigidity and disjointness for Zk actions by toral automorphisms

Boris Kalinin; Anatole Katok

doi:10.1017/S014338570200024X

Measurable rigidity and disjointness for Z^k actions by toral automorphisms

Boris Kalinin
, Anatole Katok

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We investigate joinings of strongly irreducible totally non-symplectic Anosov Z^k, k ≥ 2 actions by toral automorphisms. We show that the existence of a non-trivial joining has strong implications for these actions, in particular, that the restrictions of the actions to a finite index subgroup of Z^k are conjugate over Q. We also obtain a description of the joining measures modulo the classification of zero entropy measures for the actions.

Original language	English (US)
Title of host publication	The Collected Works of Anatole Katok
Subtitle of host publication	In 2 Volumes
Publisher	World Scientific Publishing Co.
Pages	2135-2151
Number of pages	17
Volume	2
ISBN (Electronic)	9789811238079
ISBN (Print)	9789811238062
DOIs	https://doi.org/10.1017/S014338570200024X
State	Published - Jan 1 2024

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering

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10.1017/S014338570200024X

Cite this

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abstract = "We investigate joinings of strongly irreducible totally non-symplectic Anosov Zk, k ≥ 2 actions by toral automorphisms. We show that the existence of a non-trivial joining has strong implications for these actions, in particular, that the restrictions of the actions to a finite index subgroup of Zk are conjugate over Q. We also obtain a description of the joining measures modulo the classification of zero entropy measures for the actions.",

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AB - We investigate joinings of strongly irreducible totally non-symplectic Anosov Zk, k ≥ 2 actions by toral automorphisms. We show that the existence of a non-trivial joining has strong implications for these actions, in particular, that the restrictions of the actions to a finite index subgroup of Zk are conjugate over Q. We also obtain a description of the joining measures modulo the classification of zero entropy measures for the actions.

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AN - SCOPUS:85195919959

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BT - The Collected Works of Anatole Katok

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ER -

Measurable rigidity and disjointness for Z^k actions by toral automorphisms

Abstract

All Science Journal Classification (ASJC) codes

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