Geodesic
Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
Studia Mathematica, Tome 130 (1998) no. 2, pp. 149-170

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-130-2-149-170
Keywords: almost 1-1 extension, invariant measure, isomorphism, Toeplitz flow

T. Downarowicz 1 ; Y. Lacroix 1

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T. Downarowicz; Y. Lacroix. Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows. Studia Mathematica, Tome 130 (1998) no. 2, pp. 149-170. doi: 10.4064/sm-130-2-149-170

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