Bowen's construction for the Teichmueller flow

TL;DR

This paper demonstrates that the invariant measure for the Teichmueller flow on a stratum of quadratic differentials can be constructed using Bowen's method, linking dynamical systems and Teichmueller theory.

Contribution

It establishes a novel connection between Bowen's construction and the invariant measure for the Teichmueller flow on quadratic differential strata.

Findings

Invariant measure obtained via Bowen's construction

Connection between dynamical systems and Teichmueller flow

Measure is in the Lebesgue measure class

Abstract

Let Q be a connected component of a stratum in the space of quadratic differentials for a non-exceptional Riemann surface of finite type. We show that the probability measure on Q in the Lebesgue measure class which is invariant under the Teichmueller flow is obtained by Bowen's construction.