Regularity of topological pressure: From one to two dimensional complex dynamics

CCNY Dynamical Systems Seminar

Time and place

12:30 PM on Tuesday, October 26th, 2010; NAC 6-113

Christian Wolf (CCNY)

Abstract

In this talk we study the thermodynamics of complex Henon maps which are small perturbations of one-dimensional polynomials. We derive regularity results of the generalized pressure function in a neighborhood of the degenerate map (i.e. the polynomial). We then apply these results to show uniqueness of the measure of maximal dimension as well as discontinuity of Hausdorff dimension at the boundary of the hyperbolicity locus.