Abstract:
We consider Hamiltonian systems possessing families of nonresonant invariant tori
whose frequencies are all collinear. Then under certain conditions the frequencies depend
on energy only. This is a generalization of the well-known Gordon’s theorem about periodic
solutions of Hamiltonian systems. While the proof of Gordon’s theorem uses Hamilton’s
principle, our result is based on Percival’s variational principle. This work was motivated by
the problem of isochronicity in Hamiltonian systems.
\Bibitem{BolTre23}
\by Sergey V. Bolotin, Dmitry V. Treschev
\paper Quasiperiodic Version of Gordon’s Theorem
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 1
\pages 5--13
\mathnet{http://mi.mathnet.ru/rcd1192}
\crossref{https://doi.org/10.1134/S1560354723010021}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4559066}
Linking options:
https://www.mathnet.ru/eng/rcd1192
https://www.mathnet.ru/eng/rcd/v28/i1/p5
This publication is cited in the following 2 articles:
D. V. Treschev, E. I. Kugushev, T. V. Popova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskii, “Kafedra teoreticheskoi mekhaniki i mekhatroniki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 103–113
D. V. Treschev, E. I. Kugushev, T. V. Shakhova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskiy, “Chair of Theoretical Mechanics and Mechatronics”, Moscow Univ. Mech. Bull., 79:6 (2024), 200
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