DYNAMICS OF RATIONAL FUNCTIONS WITH SIEGEL DISKS AND POLYNOMIAL SEMIGROUPS KOH KATAGATA

Abstract. This article is based on the author’s thesis, “Dynamics of rational functions and rational semigroups on the Riemann sphere”, and consists of two topics. The first topic is about Blaschke products and rational functions with Siegel disks. The second one is about Julia sets of quartic polynomials and polynomial semigroups. Throughout this article, our interest is on topological and geometrical properties of Julia sets. 1