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ArticleOriginal scientific text

Title

Isometric extensions, 2-cocycles and ergodicity of skew products

Authors 1, 2

Affiliations

  1. Department of Mechanics and Mathematics, Kharkov State University, Freedom sq. 4 Kharkov, 310077, Ukraine
  2. Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension Tα and admits a prescribed subgroup in the centralizer of Tα.

Keywords

ENG
ergodic transformation, cocycle, isometric extension

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Studia Mathematica
1999/137/2
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Pages:
123-142
Main language of publication
English
Received
1997-09-22
Accepted
1999-08-30
Published
1999
Exact and natural sciences