Minimal sets on tori

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Let Σ be a commutative semigroup of continuous endomorphisms of the r-dimensional torus. Generalizing a result of Furstenberg dealing with the circle group, necessary and sufficient conditions are given here for Σ to possess the following property: Any Σ-minimal set consists of torsion elements. Semigroups not having this property are shown to admit minimal sets of positive Hausdorff dimension.

Original languageEnglish
Pages (from-to)499-507
Number of pages9
JournalErgodic Theory and Dynamical Systems
Issue number4
StatePublished - 1 Jan 1984
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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