Exponential mixing of nilmanifold automorphisms

Alexander Gorodnik (Gorodnyk)*, Ralf Spatzier

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

11 Citations (Scopus)

Abstract

We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders. This allows us to establish probabilistic limit theorems and regularity of solutions of the cohomological equation for such automorphisms. Our method is based on the quantitative equidistribution results for polynomial maps combined with Diophantine estimates.

Original languageEnglish
Pages (from-to)355-396
Number of pages42
JournalJournal d'Analyse Mathématique
Volume123
Issue number1
DOIs
Publication statusPublished - 2014

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