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On periodic points of $\lambda$-graph systems

Published online by Cambridge University Press:  17 April 2007

KENGO MATSUMOTO
KENGO MATSUMOTO
Affiliation:
Department of Mathematical Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan (e-mail: [email protected])
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Abstract

In a previous paper (Presentations of subshifts and their topological conjugacy invariants. Doc. Math.4 (1999), 285–340), the notion of $\lambda$-graph system has been introduced. The $\lambda$-graph systems are generalizations of finite directed labeled graphs. In this paper, we study periodic points of $\lambda$-graph systems. We introduce some invariants for a $\lambda$-graph system $\mathfrak L$ to count the cardinal number of $p$-periodic points of $\mathfrak L$. They are invariant under strong shift equivalence of $\lambda$-graph systems. We then consider the zeta functions of $\lambda$-graph systems, which are also invariant under strong shift equivalence of $\lambda$-graph systems. Some examples are also presented.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 3 , June 2007 , pp. 881 - 904
Copyright
2007 Cambridge University Press

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