Kakutani equivalence for products of some special flows over rotations

ERGODIC THEORY AND DYNAMICAL SYSTEMS（2022）

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Abstract

We study Kakutani equivalence for products of some special flows over rotations with roof function smooth except a singularity at 0 is an element of 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.

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Key words

Kakutani equivalence, Kakutani invariants, special flow

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