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

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Downarowicz T., Lacroix

Studia Mathematica

1998

tom 130

nr 2

149-170

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.

Ograniczanie wyników

1 Studia Mathematica

1 Downarowicz T.

1 Lacroix

1 1998

Wyniki wyszukiwania

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