DYNAMICS IN DIMENSION ZERO A SURVEY

作者：Downarowicz Tomasz^*; Karpel Olena

来源：Discrete and Continuous Dynamical Systems, 2018, 38(3): 1033-1062.

DOI：10.3934/dcds.2018044

• Zero-dimensional dynamical systems
• symbolic extension
• Bratteli-Vershik systems

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.

• 出版日期2018-3