Geometry and Topology Seminar

Finite type maps are a class of analytic maps on complex 1-manifolds introduced by Epstein, that notably include rational maps and entire functions with a finite singular set. Each of those maps possess a natural finite-dimensional moduli space, and one can define a dynamical Teichmüller space parametrizing their quasiconformal conjugacy class. Using the fact that this Teichmüller space immerses into the moduli space, we will generalize rigidity results of Avila, Dominguez, Makienko and Sienra under an assumption of expansion along the critical orbits.