Multi-invariant measures and subsets on nilmanifolds

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)123-183
Number of pages61
JournalJournal d'Analyse Mathematique
Volume135
Issue number1
DOIs
StatePublished - Jun 1 2018

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Nilmanifolds
Invariant Measure
Subset
Obstruction
Rigidity
Probability Measure
Modulo
Automorphisms
Deduce
Entropy
Closed
Invariant
Zero

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

Cite this

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abstract = "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. / Wang, Zhiren.

In: Journal d'Analyse Mathematique, Vol. 135, No. 1, 01.06.2018, p. 123-183.

Research output: Contribution to journalArticle

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