2016/10/09 by Tomasz Downarowicz, Downarowicz, Tomasz, Olena Karpel +1
Computer Science · Mathematics · Physics and Astronomy · #37B05 #37B10 (Primary) #37B40 (Secondary) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1610.02727
openalex publication_date 2016/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to put together several techniques in handling dynamical systems on zero-dimensional spaces, such as array representation, inverse limit representation, or Bratteli-Vershik representation. We describe how one can switch from one representation to another. We also briefly review some more recent related notions: symbolic extensions, symbolic extensions with an embedding, and uniform generators. We devote a great deal of attention to marker techniques and we use them to prove two types of results: one concerning entropy and vertical data compression, and another, about the existence of isomorphic minimal models for aperiodic systems. We also introduce so-called decisiveness of Bratteli--Vershik systems and give for it a sufficient condition.