Upper bound on the rate of mixing for the Earthquake flow on moduli spaces

TL;DR

This paper establishes that the earthquake flow on moduli spaces has at most polynomial mixing rate, bounded by a topology-dependent constant, and is not exponentially mixing, providing insights into its dynamical complexity.

Contribution

The paper proves an upper bound on the polynomial rate of mixing for the earthquake flow, showing it cannot be exponentially mixing, which advances understanding of its dynamical properties.

Findings

Earthquake flow is at most polynomially mixing.

The mixing rate bound depends only on surface topology.

Earthquake flow is not exponentially mixing.

Abstract

We prove that the earthquake flow is at most polynomially mixing with a degree bounded by a constant depending only on the topology of the surface. In particular it is not exponentially mixing.