On periodic points of $\lambda$-graph systems
Kengo Matsumoto · Ergodic Theory and Dynamical Systems · 2007
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.