Drawing Limit Sets of Kleinian Groups Using Finite State Automata

Abstract

The theory of automatic groups (groups that can be treated by means offinite-stateautomata), and in particularthe techniques of automatic coset enumeration developed by Redfern, are applied to the problem of computing limit setsof a large class of Kleinian groups. We discuss in detail the case of groups in the Maskit embedding of the TeichmOller space of the punctured torus.