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Title: Constructions of smooth and analytic cocycles over irrational circle rotations (English)
Author: Volný, Dalibor
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 36
Issue: 4
Year: 1995
Pages: 745-764
Category: math
Summary: We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson, Lemańczyk, Volný]), of type $III_0$, or which are coboundaries with nonintegrable transfer functions. The cocycles are constructed as sums of coboundaries. (English)
Keyword: smooth cocycle
Keyword: real analytic cocycle
Keyword: transfer function
Keyword: type $III_0$
Keyword: ergodic and squashable
Keyword: distributions of a cocycle
MSC: 11K50
MSC: 28D05
MSC: 60F05
idZBL: Zbl 0866.28014
idMR: MR1378696
Date available: 2009-01-08T18:21:28Z
Last updated: 2012-04-30
Stable URL:
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