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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2022, том 27, выпуск 1, страницы 11–17 (Mi rcd1149)

Эта публикация цитируется в 6 статьях

On the Integrability of Circulatory Systems

Valery V. Kozlovab

a P.G. Demidov Yaroslavl State University, ul. Sovetskaya 14, 150003 Yaroslavl, Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991 Moscow, Russia

Аннотация: This paper discusses conditions for the existence of polynomial (in velocities) first integrals of the equations of motion of mechanical systems in a nonpotential force field (circulatory systems). These integrals are assumed to be single-valued smooth functions on the phase space of the system (on the space of the tangent bundle of a smooth configuration manifold). It is shown that, if the genus of the closed configuration manifold of such a system with two degrees of freedom is greater than unity, then the equations of motion admit no nonconstant single-valued polynomial integrals. Examples are given of circulatory systems with configuration space in the form of a sphere and a torus which have nontrivial polynomial laws of conservation. Some unsolved problems involved in these phenomena are discussed.

Ключевые слова: circulatory system, polynomial integral, genus of surface.

MSC: 37N05

Поступила в редакцию: 21.10.2021
Принята в печать: 27.12.2021

Язык публикации: английский

DOI: 10.1134/S1560354722010038



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