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Product of two Kochergin flows with different exponents is not standard

Volume 244 / 2019

Adam Kanigowski, Daren Wei Studia Mathematica 244 (2019), 265-283 MSC: Primary 37A35; Secondary 37A05. DOI: 10.4064/sm170218-28-8 Published online: 29 June 2018

Abstract

We study the standard (zero entropy loosely Bernoulli or loosely Kronecker) property for products of Kochergin smooth flows on $\mathbb {T}^2$ with one singularity. These flows can be represented as special flows over irrational rotations of the circle and under roof functions which are smooth on $\mathbb {T}^2\setminus \{0\}$ with a singularity at $0$. We show that there exists a full measure set $\mathscr {D}\subset \mathbb {T}$ such that the product system of two Kochergin flows with different powers of singularities and rotations from $\mathscr {D}$ is not standard.

Authors

  • Adam KanigowskiDepartment of Mathematics
    The Pennsylvania State University
    University Park, PA 16802, U.S.A.
    e-mail
  • Daren WeiDepartment of Mathematics
    The Pennsylvania State University
    University Park, PA 16802,U.S.A.
    e-mail

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