The following paper is about how a K-flow is produced from a K-induced map, but it is written in Russian. Does someone know where to find its English version? Do some textbooks include this topic?


B. Gurevič, [Certain conditions for the existence of K-decompositions for special flows](http://mi.mathnet.ru/eng/mmo192),
Tr. Mosk. Mat. Obs., 1967, Volume 17, Pages 89–116.



K-flows reference
The Gurevich paper you cite was translated as "Some Existence Conditions for K-Decompositions for Special Flows" in Trans. Moscow Math. Soc. 17 (1967), 99-128 (if you don't have access to a university library I can send a copy to you; you can find my university email address by searching my name). There is also the Totoki paper as mentioned in the [comments](https://mathoverflow.net/questions/412526/k-flows-reference#comment1057360_412526). Totoki also has a book titled *Ergodic Theory*, which includes the argument in the paper without much change it seems. Ornstein and Smorodinsky's paper "[Ergodic flows of positive entropy can be time changed to become $K$-flows](https://doi.org/10.1007/BF03007657)" has an argument very similar to Totoki's argument.


Sinai's two papers "Dynamical systems with countable Lebesgue spectrum " [I](http://dx.doi.org/10.1090/trans2/039/04) and [II](http://dx.doi.org/10.1090/trans2/068/03) are the standard references for $K$-flows.


Katok has a related paper titled "[Smooth Non-Bernoulli $K$-Automorphisms](https://www.personal.psu.edu/axk29/pub/KatokInv1980.pdf)" where he interprets the $K$-property for skew products as a cohomological equation. (This paper uses smooth structures; instead of being purely ergodic theoretical.)


Finally, most ergodic theory books don't include flows at all; one book that does is Cornfeld, Fomin, Sinai's *[Ergodic Theory](https://doi.org/10.1007/978-1-4615-6927-5)* with a special emphasis on the connection between $K$-property and spectral properties (there is also a chapter on special flows; but the connection between $K$-property for special flows and the $K$-property for the base automorphism is not developed). Nadkarni's *[Basic Ergodic Theory](https://doi.org/10.1007/978-93-86279-53-8)* also has a chapter on flows; but it does not have anything on the $K$-property.


