Two extensions of Thurston's spectral theorem for surface diffeomorphisms

TL;DR

This paper extends Thurston's spectral theorem for surface diffeomorphisms to include random products of homeomorphisms and holomorphic self-maps of Teichmüller spaces, broadening its applicability.

Contribution

It introduces new extensions of Thurston's spectral theorem, applying to random compositions and holomorphic maps in Teichmüller theory.

Findings

Extended spectral theorem to random products of homeomorphisms

Applied spectral theorem to holomorphic self-maps of Teichmüller spaces

Provided new tools for analyzing surface diffeomorphisms

Abstract

Thurston obtained a classification of individual surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichm\"uller space. In this paper we present certain extended versions of this, first, to random products of homeomorphisms and second, to holomorphic self-maps of Teichm\"uller spaces.