Kozerenko, Sergiy2025-01-272025-01-272024Kozerenko S. Dynamical structure of metric and linear self-maps on combinatorial trees / Sergiy Kozerenko // Discrete Mathematics Letters. - 2024. - Vol. 14. - P. 58-65. - https://doi.org/10.47443/dml.2024.1322664-2557https://doi.org/10.47443/dml.2024.132https://ekmair.ukma.edu.ua/handle/123456789/33336The 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.entreesperiodic pointsgraph mapsmetric mapslinear mapsMarkov graphsarticleArticle