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 he homeomorphic) are essentially preserved.
- Minimal dynamics
- Tree maps