Embedding of nonlinear dynamical systems with compact and totally disconnected domains into the product symbolic dynamical systems

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Abstract

It is known that any ε-expansive dynamical system with compact and totally disconnected domain can be embedded into a certain symbolic dynamical system. Actually, there exists a dynamical system with a compact and totally disconnected domain that cannot be topologically embedded into any symbolic dynamical system. Exactly speaking, ε-expansiveness plays an important role in the embedding problem. In this paper, the embedding theorem of dynamical systems which are not ε-expansive is discussed, and a relation between this result and the topological entropy is given.

Original languageEnglish
Pages (from-to)e1817-e1821
JournalNonlinear Analysis, Theory, Methods and Applications
Volume63
Issue number5-7
DOIs
Publication statusPublished - 30 Nov 2005

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Keywords

  • Embedding theorem
  • Lebesgue number
  • Symbolic dynamical system
  • ε-expansive dynamical system

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