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Zbl 1085.37035
Alsedà, Llu\'is; Juher, David; Mumbrú, Pere
On the preservation of combinatorial types for maps on trees. (English)
[J] Ann. Inst. Fourier 55, No. 7, 2375-2398 (2005). ISSN 0373-0956; ISSN 1777-5310/e

Summary: We study the preservation of the periodic orbits of an $A$-monotone tree map $f:T\to T$ in the class of all tree maps $g:S\to S$ having a cycle with the same pattern as $A$. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of $f$ into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees $T$ and $S$ (which need not be homeomorphic) are essentially preserved.

MSC 2000:: *37E25 Maps of trees and graphs
37E15 Combinatorial dynamics

Keywords: tree maps; minimal dynamics; combinatorial dynamics; periodic orbits; period-preserving map

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