A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Ergodicity and conservativity of products of infinite transformations and their inverses

Volume 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 Published online: 17 February 2016

Abstract

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.

Authors

  • 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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image