Journal article

Dynamical Structure Of Metric And Linear Self-Maps On Combinatorial Trees

Year:

2024

Published in:

Discrete Mathematics Letters
trees
periodic points
graph maps
metric maps
linear maps
Markov graphs

The dynamical structure of metric and linear self-maps on combinatorial trees is described. Specifically, the following question is addressed: given a map from a finite set to itself, under what conditions there exists a tree on this set such that the given map is either a metric or a linear map on this tree? The author proves that a necessary and sufficient condition for this is that the map has either a fixed point or a periodic point with period two, in which case all its periodic points must have even periods. The dynamical structure of tree automorphisms and endomorphisms is also described in a similar manner.

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