Journal article

Maps of combinatorial trees with weakly connected Markov graphs

Year:

2025

Published in:

Utilitas Mathematica
trees
maps on nite sets
periodic points
Markov graphs
weakly connected digraphs

The Markov graph of a self-map on a combinatorial tree is a directed graph that encodes the covering relations between edges of the tree under the map. This work explores the dynamical structure of self-maps on trees with weakly connected Markov graphs. The main result of the paper is a complete characterization of self-maps on finite sets that yield weakly connected Markov graphs for all trees. Additionally, we describe the dynamical structure of self-maps whose Markov graphs take specific forms, including complete digraphs, cycles, paths, in-stars, and out-stars.

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