Un diccionario entre funciones racionales y grupos de Klein.

Ponente(s): Igsyl Dominguez Calderon

Sullivan’s Dictionary provides theoretical framework to understand connections between the dynamics of rational functions and Kleinian Groups. In some cases there exist very similar proofs for results there are related in both areas . The Sullivan’s dictionary suggests several analogies which motivate the research from one area to another. This talk has the purpose to present some known results about such relations between iteration theory of rational functions and Kleinian groups. Also we present a new subject in the theory of rational functions, called the Set of Buried points and a new subject in the theory of Kleinian groups, called the Residual Limit Set, which present enough characteristics to be added to the aforementioned dictionary. In the same way results are given to show this analogy.