English

Cantor subsystems on the Gehman dendrite

Dynamical Systems 2024-11-21 v1

Abstract

In the present note we focus on dynamics on the Gehman dendrite G\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 C\mathcal{C} we provide constructions of (i) a mixing but not exact and (ii) an exact map on G\mathcal{G}, such that in both cases the subsystem formed by End(G)\text{End}(\mathcal{G}) is conjugate to the initially chosen system on C\mathcal{C}.

Cite

@article{arxiv.2411.13336,
  title  = {Cantor subsystems on the Gehman dendrite},
  author = {Piotr Oprocha and Jakub Tomaszewski},
  journal= {arXiv preprint arXiv:2411.13336},
  year   = {2024}
}
R2 v1 2026-06-28T20:06:28.104Z