Chaotic Homeomorphisms of $C$ Induced by Hyperbolic Toral Automorphisms and Branched Coverings of $\bar C$

Abstract

It is well known that there exists a regular branched covering map from $T^2$ onto $\bar C$ iff the ramification indices are $(2,2,2,$ $2)$, $(2,4,4)$, $(2,3,6)$ and $(3,3,3)$. In this paper we construct (countably many) chaotic homeomorphisms induced by hyperbolic toral automorphism and regular branched covering map corresponding to the ramification indices $(2,2,2,2)$. And we also gave an example which shows that the above construction of a chaotic map is not true in general if the ramification indices is $(2,4,4)$ and also show that there are no chaotic homeomorphisms induced by hyperbolic toral automorphism and regular branched covering map corresponding to the ramification indices $(2,3,6)$ and $(3,3,3)$.