Topological Methods in Nonlinear Analysis

Some applications of groups of essential values of cocycles in topological dynamics

Mieczysław K. Mentzen

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Abstract

A class of examples showing that a measure-theoretical characterization of regular cocycles in terms of essential values is not valid in topological dynamics is constructed. An example that in topological dynamics for the case of non-abelian groups, the groups of essential values of cohomologous cocycles need not be conjugate is given. A class of base preserving equivariant isomorphisms of Rokhlin cocycle extensions of topologically transitive flows is described. In particular, the topological centralizer of Rokhlin cocycle extension of minimal rotation defined by an action of the group $\mathbb R^m$ is determined.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 23, Number 2 (2004), 357-375.

Dates
First available in Project Euclid: 31 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1464731414

Mathematical Reviews number (MathSciNet)
MR2078197

Zentralblatt MATH identifier
1073.54019

Citation

Mentzen, Mieczysław K. Some applications of groups of essential values of cocycles in topological dynamics. Topol. Methods Nonlinear Anal. 23 (2004), no. 2, 357--375. https://projecteuclid.org/euclid.tmna/1464731414


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