Exponential Mixing of Nilmanifold Automorphisms

2012/10/08 by Alexander Gorodnik, Ralf Spatzier, Gorodnik, Alexander +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1210.2271

arxiv created 2012/10/08 · openalex publication_date 2012/10/08 · arxiv updated 2012/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• The cohomological equation for partially hyperbolic diffeomorphisms
• What an infra-nilmanifold endomorphism really should be

Cited by

• Construction of equilibrium states revisited

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• Mixing Properties of Commuting Nilmanifold Automorphisms
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