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Weak equivalence of cocycles and Mackey action in generic dynamics

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Abstract

LetR be an equivalence relation generated by a countable ergodic homeomorphism group of a perfect Polish spaceX. We consider cocycles taking values in Polish groups onR modulo meager subsets ofX. Two cocycles are called weakly equivalent if they are cohomologous up to an automorphism ofR. The notion of generic associated Mackey action is introduced, which is an invariant of weak equivalence for cocycles. Regular cocycles with values in an arbitrary Polish group and transient cocycles with values in an arbitrary countable group are completely classified up to weak equivalence.

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Authors and Affiliations

  1. School of Mathematics, University of N.S.W., 2052, Sydney, NSW, Australia

    Valentin Golodets

  2. Institute for Low Temperature Physics & Engineering, Ukrainian National Academy of Sciences, 47 Lenin Ave., 61103, Kharkov, Ukraine

    Vyacheslav Kulagin

Authors
  1. Valentin Golodets
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  2. Vyacheslav Kulagin
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Correspondence to Valentin Golodets.

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Supported in part by a CRDF grant number UM1-2092.

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Golodets, V., Kulagin, V. Weak equivalence of cocycles and Mackey action in generic dynamics. Qual. Th. Dyn. Syst. 4, 39–57 (2003). https://doi.org/10.1007/BF02972821

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