Year: 2024
Type: article
Abstract: 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.
Source: Discrete Mathematics Letters
Author: Sergiy Kozerenko
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403341186