A zeta function for flip systems

Young-One Kim, Jungseob Lee and Kyewon K. Park

Vol. 209 (2003), No. 2, 289–301

DOI: 10.2140/pjm.2003.209.289

Abstract

In this paper, we investigate dynamical systems with flip maps, which can be regarded as infinite dihedral group actions. We introduce a zeta function for flip systems, and find its basic properties including a product formula. When the underlying ℤ-action is conjugate to a topological Markov shift, the flip system is represented by a pair of matrices, and its zeta function is expressed explicitly in terms of the representation matrices.

Milestones

Received: 26 December 2001

Published: 1 April 2003