Two extensions of Thurston's spectral theorem for surface   diffeomorphisms
  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. 
Anders Karlsson
math.DS math.GT