Kakutani equivalence for products of some special flows over rotations

TL;DR

This paper investigates Kakutani equivalence among products of special flows over rotations with singular roof functions, providing estimates of invariants and identifying non-equivalent flow products.

Contribution

It introduces new estimates for Kakutani invariants for these flows and establishes a countable family of non-equivalent flow products.

Findings

Kakutani invariants estimated for flow products

Identified non-Kakutani equivalent flow products

Flow products distinguished by singularity powers

Abstract

We study Kakutani equivalence for products of some special flows over rotations with roof function smooth except a singularity at $0\in\mathbb{T}$. We estimate the Kakutani invariant for product of these flows with different powers of singularities and rotations from a full measure set. As a corollary, we obtain a countable family of pairwise non-Kakutani equivalent products of special flows over rotations.