Locally equicontinuous dynamical systems

Volume 84 / 2000

Eli Glasner, Benjamin Weiss Colloquium Mathematicum 84 (2000), 345-361 DOI: 10.4064/cm-84/85-2-345-361

Abstract

A new class of dynamical systems is defined, the class of "locally equicontinuous systems" (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in $l_{∞}(ℤ)$ form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems. Both of these inclusions are proper. The main result of the paper is to produce a family of examples of LE dynamical systems which are not WAP.

Authors

  • Eli Glasner
  • Benjamin Weiss

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