Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations

Volume 119 / 2010

Chris Dodd, Phakawa Jeasakul, Anne Jirapattanakul, Daniel M. Kane, Becky Robinson, Noah D. Stein, Cesar E. Silva Colloquium Mathematicum 119 (2010), 1-22 MSC: Primary 37A40; Secondary 37A25. DOI: 10.4064/cm119-1-1

Abstract

We define a class of discrete Abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply recurrent. We then study conditions sufficient for showing that Cartesian products of transformations are conservative for a class of invertible infinite measure-preserving transformations and provide examples of these transformations.

Authors

  • Chris DoddDepartment of Mathematics
    Massachusetts Institute of Technology
    Cambridge, MA 02139, U.S.A.
    e-mail
  • Phakawa JeasakulEconomics Department
    University of California
    Berkeley, CA 94720, U.S.A.
    e-mail
  • Anne Jirapattanakul1022 International Affairs Building
    Columbia University
    420 West 118th Street
    New York, NY 10027, U.S.A.
    e-mail
  • Daniel M. KaneDepartment of Mathematics
    Harvard University
    Cambridge, MA 02138, U.S.A.
    e-mail
  • Becky RobinsonWilliams College
    Williamstown, MA 01267, U.S.A.
    e-mail
  • Noah D. SteinLaboratory for Information and Decision Systems
    Massachusetts Institute of Technology
    Cambridge, MA 02139, U.S.A.
    e-mail
  • Cesar E. SilvaDepartment of Mathematics
    Williams College
    Williamstown, MA 01267, U.S.A.
    e-mail

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