Cantor subsystems on the Gehman dendrite

Piotr Oprocha; Jakub Tomaszewski

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arXiv · 2411.13336

Cantor subsystems on the Gehman dendrite

Piotr Oprocha·Jakub Tomaszewski

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Abstract

In the present note we focus on dynamics on the Gehman dendrite $\mathcal{G}$. It is well-known that the set of its endpoints is homeomorphic to a standard Cantor ternary set. For any given surjective Cantor system $\mathcal{C}$ we provide constructions of (i) a mixing but not exact and (ii) an exact map on $\mathcal{G}$, such that in both cases the subsystem formed by $\text{End}(\mathcal{G})$ is conjugate to the initially chosen system on $\mathcal{C}$.

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Piotr Oprocha, Jakub Tomaszewski. 2024-11-20. Cantor subsystems on the Gehman dendrite. https://arxiv.org/abs/2411.13336

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