Ergodic Theory and Dynamical Systems

Research Article

Finitely presented dynamical systems

David Frieda1

a1 Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA

Abstract

We extend results of Bowen and Manning on systems with good symbolic dynamics. In particular we identify the class of dynamical systems that admit Markov partitions. For these systems the Manning-Bowen method of counting periodic points is explained in terms of topological coincidence numbers. We show, in particular, that an expansive system with a finite cover by rectangles has a rational zeta function.

(Received October 01 1986)

(Revised January 12 1987)