Аннотация:
For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy level the principle of throwing out cycles gives periodic magnetic geodesics on the critical levels defined by the "thrown out" cycles.
Ключевые слова:
magnetic geodesics, closed extremals, calculus of variations in the large.
Поступила в редакцию: 14.01.2010 Принята в печать: 25.01.2010
Образец цитирования:
I. A. Taimanov, “Periodic magnetic geodesics on almost every energy level via variational methods”, Regul. Chaotic Dyn., 15:4-5 (2010), 598–605
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\by I. A. Taimanov
\paper Periodic magnetic geodesics on almost every energy level via variational methods
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 4-5
\pages 598--605
\mathnet{http://mi.mathnet.ru/rcd518}
\crossref{https://doi.org/10.1134/S1560354710040131}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2679767}
\zmath{https://zbmath.org/?q=an:1207.58015}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd518
https://www.mathnet.ru/rus/rcd/v15/i4/p598
Эта публикация цитируется в следующих 4 статьяx:
Wenmin Gong, “Minimax Periodic Orbits of Convex Lagrangian Systems on Complete Riemannian Manifolds”, J Geom Anal, 32:10 (2022)
Volker Branding, Wayne Rossman, “Magnetic geodesics on surfaces with singularities”, Pac. J. Math. Ind., 9:1 (2017)
GABRIELE BENEDETTI, “The contact property for symplectic magnetic fields on”, Ergod. Th. Dynam. Sys., 36:3 (2016), 682
Iskander A. Taimanov, “On an Integrable Magnetic Geodesic Flow on the Two-torus”, Regul. Chaotic Dyn., 20:6 (2015), 667–678
Цитирование в формате AMSBIB
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