Infinite measure preserving flows with infinite ergodic index

Volume 115 / 2009

Alexandre I. Danilenko, Anton V. Solomko Colloquium Mathematicum 115 (2009), 13-19 MSC: 37A40. DOI: 10.4064/cm115-1-2


We construct a rank-one infinite measure preserving flow $(T_r)_{r\in\Bbb R}$ such that for each $p>0$, the “diagonal” flow $({T_r\times\cdots\times T_r})_{r\in\Bbb R}\,(p\,{\rm times})$ on the product space is ergodic.


  • Alexandre I. DanilenkoInstitute for Low Temperature Physics
    & Engineering
    National Academy of Sciences of Ukraine
    47 Lenin Ave.
    Kharkov, 61164, Ukraine
  • Anton V. SolomkoDepartment of Mathematics
    and Mechanical Engineering
    Kharkov National University
    4 Freedom sq.
    Kharkov, 61077, Ukraine

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