Two extensions of Thurston's spectral theorem for surface diffeomorphisms

Abstract

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

11 pages

References in corpus (1)

• On laws of large numbers for random walks

Cited by in corpus (4)

• Central limit theorems for mapping class groups and $\text{Out}(F_N)$
• Spectral theorems for random walks on mapping class groups and $\text{Out}(F_N)$
• Horofunction compactifications and duality
• Central limit theorem and geodesic tracking on hyperbolic spaces and Teichmüller spaces