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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 1108–1124
DOI: https://doi.org/10.33048/semi.2023.20.069
(Mi semr1632)
 

Differentical equations, dynamical systems and optimal control

Algebraic ovals and rational integrals of Darboux-type systems

E. P. Volokitin, V. M. Cheresiz

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: We consider the question of the existence of algebraic solutions, polynomial and rational integrals for systems of ordinary differential equations of the form $\dot x=x+P_n(x,y),\ \dot y=y+Q_n(x,y)$, where $P_n(x,y), $ $Q_n(x,y)$ are homogeneous polynomials of $n$th degree.
Keywords: polynomial systems, algebraic limit cycles, non-algebraic limit cycles, rational integrals, phase portraits.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0005
FWNF-2022-0008
Received August 1, 2022, published November 24, 2023
Document Type: Article
UDC: 517.925
MSC: 34C05
Language: Russian
Citation: E. P. Volokitin, V. M. Cheresiz, “Algebraic ovals and rational integrals of Darboux-type systems”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1108–1124
Citation in format AMSBIB
\Bibitem{VolChe23}
\by E.~P.~Volokitin, V.~M.~Cheresiz
\paper Algebraic ovals and rational integrals of Darboux-type systems
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 1108--1124
\mathnet{http://mi.mathnet.ru/semr1632}
\crossref{https://doi.org/10.33048/semi.2023.20.069}
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