Exponential mixing of the Teichm\"uller flow on affine invariant manifolds

TL;DR

This paper provides a new proof demonstrating that the Teichmüller flow exhibits exponential mixing behavior with respect to any ergodic SL(2,R)-invariant measure on non-exceptional surfaces, enhancing understanding of its dynamical properties.

Contribution

The paper introduces a novel proof technique based on symbolic coding to establish exponential mixing of the Teichmüller flow, building on and simplifying previous results by Avila and Gouezel.

Findings

Teichmüller flow is exponentially mixing for non-exceptional surfaces.

The proof employs symbolic coding methods.

Results apply to any ergodic SL(2,R)-invariant measure.

Abstract

Let S be a non-exceptional oriented surface of finite type. We give a new proof based on symbolic coding of the following result of Avila and Gouezel. The Teichmueller flow is exponentially mixing with respect to any ergodic SL(2,R)-invariant Borel probability measure.