Geodesic
Instability of Equilibria in a Solenoidal Force Field
Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 207-216

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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, equilibrium, asymptotic solution, quasihomogeneous system.
Mots-clés : covariant divergence 
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     author = {V. V. Kozlov},
     title = {Instability of {Equilibria} in a {Solenoidal} {Force} {Field}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {207--216},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a4/}
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V. V. Kozlov. Instability of Equilibria in a Solenoidal Force Field. Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 207-216. http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a4/