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ArticleOriginal scientific text

Title

Construction of non-constant and ergodic cocycles

Authors 1

Affiliations

  1. Department of Mathematics, Rutgers University, Camden, NJ 08102, U.S.A.

Abstract

We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on the "closure of coboundaries technique", whereas the second result is proved by developing in addition a new approximation technique.

Keywords

ENG
cocycles, rigid dynamical systems, ergodicity

Bibliography

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Colloquium Mathematicum
2000/84/85/2
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Pages:
395-419
Main language of publication
English
Received
1999-08-20
Accepted
2000-02-02
Published
2000
Exact and natural sciences