TODORČEVIĆ’ TRICHOTOMY AND A HIERARCHY IN THE CLASS OF TAME DYNAMICAL SYSTEMS

Eli Glasner, Michael Megrelishvili

Research output: Contribution to journalArticlepeer-review

Abstract

Todorčević’ trichotomy in the class of separable Rosenthal compacta induces a hierarchy in the class of tame (compact, metrizable) dynamical systems (X,T) according to the topological properties of their enveloping semigroups E(X). More precisely, we define the classes Tame2 ⊂ Tame1 ⊂ Tame, where Tame1 is the proper subclass of tame systems with first countable E(X), and Tame2 is its proper subclass consisting of systems with hereditarily separable E(X). We study some general properties of these classes and exhibit many examples to illustrate these properties.

Original languageEnglish
Pages (from-to)4513-4548
Number of pages36
JournalTransactions of the American Mathematical Society
Volume375
Issue number7
DOIs
StatePublished - 1 Jul 2022

Keywords

  • Almost automorphic system
  • Rosenthal compact
  • Sturmian system
  • circular order
  • enveloping semigroup
  • linear order
  • tame dynamical system

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