Multi-invariant sets on compact abelian groups

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31 Scopus citations

Abstract

Let G be a finite-dimensional connected compact abelian group. Generalizing previous results, dealing with the case of finite-dimensional tori, a full characterization is given herewith of those commutative semigroups 2 of continuous endomorphisms Σ of G which satisfy the following property: The only infinite closed Σ-invariant subset of G is G itself.

Original languageEnglish
Pages (from-to)505-535
Number of pages31
JournalTransactions of the American Mathematical Society
Volume286
Issue number2
DOIs
StatePublished - 1 Jan 1984
Externally publishedYes

Keywords

  • Ergodic endomorphism
  • Finite-dimensional group
  • Invariant set
  • Minimal flow
  • Multi-parameter flow
  • Semigroup of endomorphisms
  • Solenoid

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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