| Abstract: |
| Markov-Dyck shifts are symbolic dynamical systems, that are constructed from %strongly connected finite directed graphs. The inverse semigroup of the graph appears as an intermediate step in this construction. We consider Markov-Dyck shifts, that are constructed from strongly connected finite directed graphs, such that by removing all edges from the graph, whose target vertex has more than one incoming edge, one obtains a tree. This tree we call the contracting subtree of the graph. We consider certain families of graphs with a contracting subtree. We characterize the Markov-Dyck shifts of the graphs, that belong to these families, among Markov-Dyck shifts, by invariants of topological conjugacy. We also show for the graphs in these families, that the topological conjugacy of their Markov-Dyck shifts implies the isomorphism of the graphs. Among the families, that we consider, is the family of graphs, whose contracting subtree is spherically homogeneous of depth two. We also consider families, that contain graphs with four edges in the complement of their contracting subtrees. In the proofs we use semigroup invariants and periodic orbit counts. |
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