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Matematicheskie Zametki, 2023, Volume 113, Issue 2, Pages 207–216
DOI: https://doi.org/10.4213/mzm13884 (Mi mzm13884) 		 
Instability of Equilibria in a Solenoidal Force Field

V. V. Kozlovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b P.G. Demidov Yaroslavl State University
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DOI: https://doi.org/10.4213/mzm13884
Abstract: We discuss the conjecture that an isolated equilibrium of a mechanical system in a solenoidal force field is unstable. A number of statements confirming this conjecture under additional general position conditions guaranteeing that the equilibrium is isolated are proved. More precisely, we prove that there exist phase trajectories asymptotically leaving the equilibrium state.
Keywords: solenoidal field, covariant divergence, equilibrium, asymptotic solution, quasihomogeneous system.
Funding agency Grant number
Russian Science Foundation 21-71-30011
This work was supported by the Russian Science Foundation under grant 21-71-30011, https://rscf.ru/project/21-71-30011/.
Received: 09.09.2022
English version:
Mathematical Notes, 2023, Volume 113, Issue 2, Pages 220–227
DOI: https://doi.org/10.1134/S000143462301025X
Bibliographic databases:
Document Type: Article
UDC: 517.9+531.36
Language: Russian
Citation: V. V. Kozlov, “Instability of Equilibria in a Solenoidal Force Field”, Mat. Zametki, 113:2 (2023), 207–216; Math. Notes, 113:2 (2023), 220–227
Citation in format AMSBIB
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\by V.~V.~Kozlov
\paper Instability of Equilibria in a Solenoidal Force Field
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 2
\pages 207--216
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\crossref{https://doi.org/10.4213/mzm13884}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563363}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 2
\pages 220--227
\crossref{https://doi.org/10.1134/S000143462301025X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149685350}
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