Orthogonal polynomials on generalized Julia sets

Abstract

We extend results by Barnsley et al. about orthogonal polynomials on Julia sets to the case of generalized Julia sets. The equilibrium measure is considered. In addition, we discuss optimal smoothness of Green functions and Parreau-Widom criterion for a special family of real generalized Julia sets.

We changed the second part of the article a little bit and gave sharper results in this version