Function theory, Dynamics and Ergodic theory via Thurston theory

Abstract

In this paper, we discuss function theory on Teichmüller space through Thurston's theory, as well as the dynamics of subgroups of the mapping class group of a surface, with reference to Sullivan's theory on the ergodic actions of discrete subgroups of the isometry group of hyperbolic space at infinity.

This is written as a chapter of a book