Multi-invariant sets on tori Academic Article uri icon


  • Given a compact metric group $G$, we are interested in those semigroups $\Sigma$ of continuous endomorphisms of $G$, possessing the following property: The only infinite, closed, $\Sigma$-invariant subset of $G$ is $G$ itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization--for the case of finite-dimensional tori--of those commutative semigroups with the aforementioned property.

publication date

  • January 1, 1983