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Smooth cocycles for an irrational rotation

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Abstract

Explicit examples of smooth cocycles not cohomologous to constants are constructed. Necessary and sufficient conditions on the irrational numberθ are given for the existence of such cocycles. It is shown that, depending onθ, the set ofC r cocycles whose skew-product is ergodic is either residual or empty.

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Authors and Affiliations

  1. Department of Mathmatics, University of Colorado at Boulder, Campus Box 426, 80309-0426, Boulder, Colorado, USA

    L. Baggett

  2. Department of Mathematics, The Colorado College, 80903, Colorado Springs, Colorado, USA

    K. Merrill

Authors
  1. L. Baggett
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  2. K. Merrill
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Baggett, L., Merrill, K. Smooth cocycles for an irrational rotation. Israel J. Math. 79, 281–288 (1992). https://doi.org/10.1007/BF02808220

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  • DOI: https://doi.org/10.1007/BF02808220

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