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Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows

Tom 130 / 1998

T. Downarowicz, Y. Lacroix Studia Mathematica 130 (1998), 149-170 DOI: 10.4064/sm-130-2-149-170

Streszczenie

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.

Autorzy

  • T. Downarowicz
  • Y. Lacroix

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