Zeta functions and topological entropy of the Markov-Dyck shifts
Wolfgang Krieger, Kengo Matsumoto
TL;DR
This paper derives a formula for the zeta function of Markov-Dyck shifts from finite directed graphs and computes the topological entropy for specific examples including the Fibonacci-Dyck shift.
Contribution
It provides a new expression for the zeta function of Markov-Dyck shifts and calculates their topological entropy for particular cases.
Findings
Derived explicit zeta function formula for Markov-Dyck shifts
Computed topological entropy for Fibonacci-Dyck shift
Extended understanding of dynamical properties of graph-based shifts
Abstract
The Markov-Dyck shifts arise from finite directed graphs. An expression for the zeta function of a Markov-Dyck shift is given. The derivation of this expression is based on a formula in Keller (G. Keller, {\it Circular codes, loop counting, and zeta-functions}, J. Combinatorial Theory {\bf 56} (1991), pp. 75--83). For a class of examples that includes the Fibonacci-Dyck shift the zeta functions and topological entropy ae determined.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quasicrystal Structures and Properties · Cellular Automata and Applications