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Artin Mazur zeta function on trees with infinite branches
by
João Ferreira Alves
Dep de Matemática - Instituto Superior Técnico - Lisbon
Coauthors: José Sousa Ramos
One of extremely useful tools for studying the periodic structure of a dynamical system was introduced by Artin and Mazur. Let X be an arbitrary set and f:X --> X any map. Suppose that each positive iterate fn has only finitely many fixed points, then one defines the of f, \zeta(z), to be the formal power series where \QTRrmFix(fn) denotes the set of all fixed points of fn. Later on, several variants of this notion were introduced by different authors. In the general problem of computing \zeta(z), Milnor and Thurston showed that, for any expanding piecewise monotone interval map, \zeta(z) can be computed in terms of its kneading data. Recently were obtained generalizations of this result for finite trees and graphs. In this paper we present a non trivial generalization of the same result for trees with finitely many branching points and infinite branches.
Date received: March 11, 2004
Copyright © 2004 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 # canu-36.