Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
Volume 130 / 1998
Studia Mathematica 130 (1998), 149-170
DOI: 10.4064/sm-130-2-149-170
Abstract
Let $(Z,T_Z)$ be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of $(Z,T_Z)$ is Borel isomorphic to an almost 1-1 extension of $(Z,T_Z)$. Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly ergodic toeplitz flow.
