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The minimum tree for a given zero-entropy period.

Barrabés, Esther; Juher, David — 2005

International Journal of Mathematics and Mathematical Sciences

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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