Product of two Kochergin flows with different exponents is not standard
Volume 244 / 2019
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.
