Cantor subsystems on the Gehman dendrite

2024/11/20 by Piotr Oprocha, Oprocha, Piotr, Jakub Tomaszewski +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Neural Networks and Applications #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2411.13336

openalex publication_date 2024/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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