On the Markov-Dyck shifts of vertex type

Kengo Matsumoto

doi:10.3934/dcds.2016.36.403

Article Contents

2016, Volume 36, Issue 1: 403-422. Doi: 10.3934/dcds.2016.36.403

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On the Markov-Dyck shifts of vertex type

Kengo Matsumoto^1,

1.
Department of Mathematics, Joetsu University of Education, Joetsu 943-8512

Received: May 2014

Revised: April 2015

Published: May 2017

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Abstract

For a given finite directed graph $G$, there are two types of Markov-Dyck shifts, the Markov-Dyck shift $D_G^V$ of vertex type and the Markov-Dyck shift $D_G^E$ of edge type. It is shown that, if $G$ does not have multi-edges, the former is a finite-to-one factor of the latter, and they have the same topological entropy. An expression for the zeta function of a Markov-Dyck shift of vertex type is given. It is different from that of the Markov-Dyck shift of edge type.

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Mathematics Subject Classification: Primary: 37B10; Secondary: 46L05, 05A15.

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