Krasnoselskii, Perov, Povolotskiy, Zabreyko. Plane Vector Fields (Vektornye polya na ploskosti). First edition, 1963. In Russian.

Красносельский, Марк Александрович ; Перов, Анатолий Иванович ; Поволоцкий, Абрам Исаакович ; Забрейко, Петр Петрович. Векторные поля на плоскости / редактор М. М. Горячая.
Москва : Государственное издательство физико-математической литературы «Физматгиз», 1963. 248 страниц, с иллюстрациями ; 20 см. Тираж 11 000 экз.
Твердый издательский переплет.
Состояние хорошее: переплет чистый, светлая ткань без пятен; небольшая заминка у верхнего края корешка. Блок крепкий, титульные страницы чистые.
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Krasnoselskii, Mark Alexandrovich ; Perov, Anatoliy Ivanovich ; Povolotskiy, Abram Isaakovich ; Zabreyko, Pyotr Petrovich. Plane Vector Fields / editor M. M. Goryachaya. First edition.
Moscow : State Publishing House of Physical and Mathematical Literature "Fizmatgiz", 1963. 248 pp. : illustrations ; 20 cm. Print run of 11,000 copies.
Hardcover.
Condition good: boards clean, light-coloured cloth unstained; small crease at the upper edge of the spine. Text block firm, title pages clean.

A foundational Soviet monograph on the geometric theory of vector field rotation and its applications across polynomial algebra, function theory, and the theory of ordinary differential equations, authored by Mark Alexandrovich Krasnoselskii (1920-1997), the leading Soviet figure in nonlinear functional analysis and fixed-point theory, together with three of his close collaborators. The book develops the rotation of a vector field and the index of a singular point from first principles, through angular functions and the Poincare formula, before proceeding to vector fields with principal linear and polylinear parts, homotopy methods, and degree theory for mappings, laying essential groundwork for the fixed-point and topological methods that Krasnoselskii's school would go on to apply throughout nonlinear analysis. As the annotation notes, a number of the results presented belong to the authors themselves rather than being drawn from prior literature. The book was subsequently translated into English (as Plane Vector Fields, Academic Press) and remains a standard reference for specialists in nonlinear functional analysis, degree theory, and the topological methods used in the qualitative theory of differential equations, as well as a text of interest to historians tracing the development of the Voronezh-Moscow school of nonlinear analysis founded by Krasnoselskii.