On periodic points of $\lambda$-graph systems

• Autores: Kengo Matsumoto
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 3, 2007, págs. 881-904
• Idioma: inglés
• DOI: 10.1017/s0143385706001076
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• Resumen

  • 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.