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Ergodicity and conservativity of products of infinite transformations and their inverses

Tom 143 / 2016

Julien Clancy, Rina Friedberg, Indraneel Kasmalkar, Isaac Loh, Tudor Pădurariu, Cesar E. Silva, Sahana Vasudevan Colloquium Mathematicum 143 (2016), 271-291 MSC: Primary 37A40; Secondary 37A05, 37A50. DOI: 10.4064/cm6482-10-2015 Opublikowany online: 17 February 2016

Streszczenie

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ is ergodic, but the product $T\times T^{-1}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.

Autorzy

  • Julien ClancyYale University
    New Haven, CT 06520, U.S.A.
    e-mail
  • Rina FriedbergUniversity of Chicago
    Chicago, IL 60637, U.S.A.
    e-mail
  • Indraneel KasmalkarUniversity of California, Berkeley
    Berkeley, CA 94720, U.S.A.
    e-mail
  • Isaac LohWilliams College
    Williamstown, MA 01267, U.S.A.
    e-mail
  • Tudor PădurariuUniversity of California
    Los Angeles, CA 90095-1555, U.S.A.
    e-mail
  • Cesar E. SilvaDepartment of Mathematics
    Williams College
    Williamstown, MA 01267, U.S.A.
    e-mail
  • Sahana VasudevanHarvard University
    Cambridge, MA 02138, U.S.A.
    e-mail

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