Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 225, Pages 123–133
DOI: https://doi.org/10.36535/0233-6723-2023-225-123-133 (Mi into1193) 		 
On an exact estimate of the number of real invariant lines of polynomial vector fields of degree $n$

A. D. Ushkho, V. B. Tlyachev, D. S. Ushkho

Adyghe State University, Maikop
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DOI: https://doi.org/10.36535/0233-6723-2023-225-123-133
Abstract: In this paper, we prove that a polynomial vector field of degree $n$ that has two invariant sets, each of which consists of ${n-1}$ pairwise real invariant straight lines, has at most ${2n+4}$ invariant straight lines, where $n$ is odd and $n\geq3$.
Keywords: polynomial vector field, invariant straight line, invariant set, nodal point, rectangle, golden ratio.
Document Type: Article
UDC: 517.91, 514.742.4
MSC: 34C14, 34A26
Language: Russian
Citation: A. D. Ushkho, V. B. Tlyachev, D. S. Ushkho, “On an exact estimate of the number of real invariant lines of polynomial vector fields of degree $n$”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 225, VINITI, Moscow, 2023, 123–133
Citation in format AMSBIB
\Bibitem{UshTlyUsh23}
\by A.~D.~Ushkho, V.~B.~Tlyachev, D.~S.~Ushkho
\paper On an exact estimate of the number of real invariant lines of polynomial vector fields of degree $n$
\inbook Differential Equations and Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 225
\pages 123--133
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1193}
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