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Dynamics in dimension zero A survey

The second author is supported by the NCN (National Science Center, Poland) Grant 2013/08/A/ST1/00275

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  • 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.

    Mathematics Subject Classification: Primary: 37B05, 37B10; Secondary: 37B40.

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