Abstract:
In this paper we prove a Nekhoroshev type theorem for perturbations of Hamiltonians describing a particle subject to the force due to a central potential. Precisely, we prove that under an explicit condition on the potential, the Hamiltonian of the central motion is quasiconvex. Thus, when it is perturbed, two actions (the modulus of the total angular momentum and the action of the reduced radial system) are approximately conserved for times which are exponentially long with the inverse of the perturbation parameter.
Keywords:
Nekhoroshev theorem, central motion, Hamiltonian dynamics.
\Bibitem{BamFus17}
\by Dario Bambusi, Alessandra Fus\`e
\paper Nekhoroshev Theorem for Perturbations of the Central Motion
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 1
\pages 18--26
\mathnet{http://mi.mathnet.ru/rcd241}
\crossref{https://doi.org/10.1134/S1560354717010026}
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Linking options:
https://www.mathnet.ru/eng/rcd241
https://www.mathnet.ru/eng/rcd/v22/i1/p18
This publication is cited in the following 4 articles:
Dario Bambusi, Beatrice Langella, Marc Rouveyrol, “On the Stable Eigenvalues of Perturbed Anharmonic Oscillators in Dimension Two”, Commun. Math. Phys., 390:1 (2022), 309
I. De Blasi, A. Celletti, Ch. Efthymiopoulos, “Semi-analytical estimates for the orbital stability of Earth's satellites”, J. Nonlinear Sci., 31:6 (2021), 93
L. Mi, W. Cui, H. You, “Periodic and quasi-periodic solutions for the complex swift-hohenberg equation”, J. Appl. Anal. Comput., 10:1 (2020), 297–313
Dario Bambusi, Alessandra Fusè, Marco Sansottera, “Exponential Stability in the Perturbed Central Force Problem”, Regul. Chaotic Dyn., 23:7-8 (2018), 821–841
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