Abstract:

About 100 years ago, Fatou and Julia have laid out the basic principles of iteration of holomorphic functions. Since then several attempts have been made to generalize their ideas. E.g. Barnsley and Demko have started the development of a theory of multivalued iteration leading to a function system generated by branches of an algebraic relation. Later Rasch has provided a framework that can be used to study both, forward and backward iteration of rational functions. In this talk an approach towards unifying the theory of algebraic relations and the classical iteration theory of transcendental functions will be discussed. (Joint work with Christian Bick)