Michael Handel, Bruce Kitchens, et al.
Israel Journal of Mathematics
An irreducible algebraic ℤd -action α on a compact abelian group X is a ℤd-action by automorphisms of X such that every closed, α-invariant subgroup Y X is finite. We prove the following result: if d ≥ 2, then every measurable conjugacy between irreducible and mixing algebraic ℤd-actions on compact zero-dimensional abelian groups is affine. For irreducible, expansive and mixing algebraic ℤd-actions on compact connected abelian groups the analogous statement follows essentially from a result by Katok and Spatzier on invariant measures of such actions (cf. [4] and [3]). By combining these two theorems one obtains isomorphism rigidity of all irreducible, expansive and mixing algebraic ℤd-actions with d ≥ 2.
Michael Handel, Bruce Kitchens, et al.
Israel Journal of Mathematics
Bruce Kitchens, Klaus Schmidt
Ergodic Theory and Dynamical Systems
Bruce Kitchens, Selim Tuncel
Israel Journal of Mathematics
Bruce Kitchens, Klaus Schmidt
Ergodic Theory and Dynamical Systems