2016/06/01 by Takashi Shimomura, Shimomura, Takashi
Computer Science · Mathematics · #37B05 #37B10 #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1606.00296
openalex publication_date 2016/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank K > 1 is expansive. Bezuglyi, Kwiatkowski, and Medynets (2009) extended the result to non-minimal aperiodic cases. In this paper, we show that all finite-rank zero-dimensional systems are expansive or have infinite odometer systems; this is an extension of the two aforementioned results. Nevertheless, the methods follow similar approaches.