Surface homeomorphisms and graph endomorphisms
by
André de Carvalho
University of California at Berkeley

We will present a way to relate the dynamics of surface homeomorphisms and that of graph endomorphisms. We will also present deformation theories for both kinds of dynamical systems which correspond under the the relation we define. In the 2 dimensional case, the deformation theory is called pruning theory. It describes a way of isotoping a surface homeomorphism so as to destroy dynamics in a controlled fashion. In dimension 1, the deformation theory is a generalized kneading theory for graph endomorphisms.

Along the way, we mention a way to improve the algorithmic proofs given by Bestvina and Handel and Misiurewicz and Franks of Thurston's classification theorem for surface homeomorphisms up to isotopy.

Date received: February 27, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caam-28.