Kakutani equivalence for products of some special flows over rotations

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 products 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.

Flow–orbit equivalence for minimal Cantor systems

This paper is about flow–orbit equivalence, a topological analog of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a flow–orbit equivalence. We also describe the relationship between flow–orbit equivalence and a distortion function of an orbit equivalence. We show that, if the distortion of an orbit equivalence is zero, then it is in fact a flow–orbit equivalence, and that the converse is true up to a conjugation by an element of the full group.