Date:	Tue, September 30, 2014
Time:	14:15
Place:	Resnikoff Mathematics Lounge

Abstract: By classical works of Bowen and Ruelle, it is known that the Hausdorff dimension of Julia sets depend real-analytically on the parameters in the hyperbolic components of polynomials. The key ingredients of Ruelle's proof are the structural stability and the expanding property of these maps inside the hyperbolic components.

In this talk, we will outline a proof of real-analyticity of HD of Julia sets on some special regions of the bifurcation locus where the maps are 'semi-stable' and 'expansive'. As an application, we will show that the HD is a real-analytic function of Ecalle height along the parabolic arcs of the multicorns.