Multi-invariant measures and subsets on nilmanifolds

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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.

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

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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