Product of two Kochergin flows with different exponents is not standard

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 $\mathcal{D}\subset \mathbb{T}$ such that the product system of two Kochergin flows with different power of singularities and rotations from $\mathcal{D}$ is not standard.

Revised version, to appear in Studia Mathematica

Cited by in corpus (2)

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• Kakutani equivalence for products of some special flows over rotations