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On the preservation of combinatorial types for maps on trees

Lluís Alsedà;  David Juher;  Pere Mumbrú — 2005

Annales de l'institut Fourier

We study the preservation of the periodic orbits of an A -monotone tree map f : T ⟶ T in the class of all tree maps g : S ⟶ 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.

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