A note on the definition of good special flows of Kanigowski and Ravotti

Abstract

In this short note we show that certain definition from the work of Kanigowski and Ravotti can be relaxed. More specifically, we show that the definition of good special flows, that is, flows exhibiting a form of mechanism of mixing, shearing of Birkhoff sums can be relaxed. Specifically, we show that the disintegration corresponding to almost partitions, which are uniformly sheared along the direction of the flow, of the base can depend on $k$-tuple of times. This note serves as a complementary material to an article on mixing of higher order in flows of the author (details in the note), where we use the new definition of good special flows to show that flows of Fayad on $n$-torus, $n\geq 3$, are mixing of any order.