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LSpice
LSpice
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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 commentscomments. 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""Ergodic flows of positive entropy can be time changed to become $K$-flows" has an argument very similar to Totoki's argument.

Sinai's two papers "Dynamical systems with countable Lebesgue spectrum " II and IIII are the standard references for $K$-flows (see https://www.ams.org/books/trans2/039/ and https://www.ams.org/books/trans2/068/).

Katok has a related paper titled "Smooth Non-Bernoulli $K$-Automorphisms" ("https://www.personal.psu.edu/axk29/pub/KatokInv1980.pdfSmooth Non-Bernoulli $K$-Automorphisms)" 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 TheoryErgodic Theory 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 TheoryBasic Ergodic Theory also has a chapter on flows; but it does not have anything on the $K$-property.

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. 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" has an argument very similar to Totoki's argument.

Sinai's two papers "Dynamical systems with countable Lebesgue spectrum " I and II are the standard references for $K$-flows (see https://www.ams.org/books/trans2/039/ and https://www.ams.org/books/trans2/068/).

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 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 also has a chapter on flows; but it does not have anything on the $K$-property.

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. 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" has an argument very similar to Totoki's argument.

Sinai's two papers "Dynamical systems with countable Lebesgue spectrum " I and II are the standard references for $K$-flows.

Katok has a related paper titled "Smooth Non-Bernoulli $K$-Automorphisms" 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 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 also has a chapter on flows; but it does not have anything on the $K$-property.

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Alp Uzman
Alp Uzman
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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. 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" has an argument very similar to Totoki's argument.

Sinai's two papers "Dynamical systems with countable Lebesgue spectrum " I and II are the standard references for $K$-flows (see https://www.ams.org/books/trans2/039/ and https://www.ams.org/books/trans2/068/).

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 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 also has a chapter on flows; but it does not have anything on the $K$-property.