Rigidity properties of ℤd-actions on tori and solenoids

Manfred Einsiedler, Elon Lindenstrauss

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We show that Haar measure is a unique measure on a torus or more generally a solenoid X invariant under a not virtually cyclic totally irreducible ℤd-action by automorphisms of X such that at least one element of the action acts with positive entropy. We also give a corresponding theorem in the nonirreducible case. These results have applications regarding measurable factors and joinings of these algebraic ℤd-actions.

Original languageAmerican English
Pages (from-to)99-110
Number of pages12
JournalElectronic Research Announcements of the American Mathematical Society
Issue number13
StatePublished - 14 Oct 2003
Externally publishedYes


  • Entropy
  • Invariant measures
  • Invariant σ-algebras
  • Joinings
  • Measurable factors
  • Solenoid automorphism
  • Toral automorphisms


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