Geodesic
Construction of non-constant and ergodic cocycles
Colloquium Mathematicum, Tome 84 (2000) no. 2, pp. 395-419

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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.
DOI : 10.4064/cm-84/85-2-395-419
Keywords: cocycles, rigid dynamical systems, ergodicity

Mahesh Nerurkar 1

1 
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Mahesh Nerurkar. Construction of non-constant and ergodic cocycles. Colloquium Mathematicum, Tome 84 (2000) no. 2, pp. 395-419. doi: 10.4064/cm-84/85-2-395-419

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