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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Technical University, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  2. Département de Mathématiques, Faculté des Sciences, Université de Bretagne Occidentale, 6 Avenue V. Le Gorgeu, B.P. 809, 29285 Brest Cedex, France

Abstract

Let (Z,TZ) be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of (Z,TZ) is Borel isomorphic to an almost 1-1 extension of (Z,TZ). 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.

Keywords

ENG
almost 1-1 extension, invariant measure, isomorphism, Toeplitz flow

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Studia Mathematica
1998/130/2
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Pages:
149-170
Main language of publication
English
Received
1997-04-06
Accepted
1997-11-19
Published
1998
Exact and natural sciences