Bers and Hénon, Painlevé and Schrödinger

Serge Cantat
2009 Duke mathematical journal  
In this paper, we pursue the study of the holomorphic dynamics of mapping class groups on 2-dimensional character varieties, also called trace-maps dynamics in the literature, as initiated in [44] (see also [20] ). We shall show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of Hénon mappings, and then apply this idea to answer open questions concerning (1) the geometry of discrete and faithful representations of free groups into SL(2, C), (2) the
more » ... of Painlevé sixth equations, and (3) the spectrum of certain discrete Schrödinger operators. Date: 2007.
doi:10.1215/00127094-2009-042 fatcat:5vplftdk4jcmnikrjxuewpjfhu