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Minimal dynamics for tree maps

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  • We prove that, given a tree pattern $\mathcal{P}$, the set of periods of a minimal representative $f: T\rightarrow T$ of $\mathcal{P}$ is contained in the set of periods of any other representative. This statement is an immediate corollary of the following stronger result: there is a period-preserving injection from the set of periodic points of $f$ into that of any other representative of $\mathcal{P}$. We prove this result by extending the main theorem of [6] to negative cycles.
    Mathematics Subject Classification: Primary: 37E25.

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