Multi-invariant measures and subsets on nilmanifolds

Zhiren Wang

doi:10.1007/s11854-018-0041-z

Multi-invariant measures and subsets on nilmanifolds

Zhiren Wang

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Given a Z^r-action α on a nilmanifold X by automorphisms and an ergodic α-invariant probability measure μ, we show that μ is the uniform measure on X unless, modulo finite index modification, one of the following obstructions occurs for an algebraic factor action(1)the factor measure has zero entropy under every element of the action(2)the factor action is virtually cyclic.We also deduce a rigidity property for invariant closed subsets.

Original language	English (US)
Pages (from-to)	123-183
Number of pages	61
Journal	Journal d'Analyse Mathematique
Volume	135
Issue number	1
DOIs	https://doi.org/10.1007/s11854-018-0041-z
State	Published - Jun 1 2018

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics

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10.1007/s11854-018-0041-z

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AB - Given a Zr-action α on a nilmanifold X by automorphisms and an ergodic α-invariant probability measure μ, we show that μ is the uniform measure on X unless, modulo finite index modification, one of the following obstructions occurs for an algebraic factor action(1)the factor measure has zero entropy under every element of the action(2)the factor action is virtually cyclic.We also deduce a rigidity property for invariant closed subsets.

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Multi-invariant measures and subsets on nilmanifolds

Abstract

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