Abstract
We start with a relativistic model of the Kepler Problem, which is an isoenergetically non-degenerate central force problem in 2 dimensions. Then we prove the persistence of invariant cylinders and tori for a class of non Hamiltonian perturbations of this system.
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References
R. Abraham and J. Marsden, “Foundations of Mechanics,” Benjamin, Reading, Mass, 1978.
V.I. Arnold, Mathematical Methods of Classical Mechanics,MIR (russian) (1975), Moscow; (english) (1978), Springer-Verlag, New York.
V.I. Arnold, Proof of A.N. Kolmogorov’s theorem on the perturbation of quasi-per- iodic motions under small perturbations of the Hamiltonian, (russian) Usp. Mat. Nauk SSSR 18 (1963), 13–40; (english) Russian Math. Surveys 18(1963), 9–36.
V.I. Arnold, V.V. Kozlov and A.I. Neishtadt, Mathematical aspects of classical and Celestial Mechanics, Encyclopedia of Mathematical Sciences, vol. 3(1988), Springer-Verlag, Berlin.
P.G. Bergmann, “Introduction to the Theory of Relativity,” Dover, New York, 1976.
M.R. Herman, Sur les courbes invariantes par les difféomorphismesde l’anneau, Astérisque 144(1986).
J. Liouville, Sur Vintegration des equations différentielles de la dynamique, J. de Math. Pures et Appl. 20(1855), 137–138.
L. Markus and K.R. Meyer, Generic Hamiltonian dynamical systems are neither integrable non ergodic, Memoirs of the Amer. Math. Soc. 144(1974).
R. McGehee, Triple collision in the collinear three-body problem, Invent iones Math. 27(1974), 191–227.
J. Moser, “Stable and random motion in dynamical systems,” Princeton Univ. Press, Princeton, 1973.
D. Park, Classical Dynamics and its quantum analogues,Lecture Notes in Physics 110 (1979), Springer-Verlag, New York.
W. Thirring, “A Course in Mathematical Physics I, Classical Dynamical Systems,” Springer Verlag, 1978, New York.
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© 1991 Springer-Verlag New York, Inc.
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Lacomba, E.A., Llibre, J., Nunes, A. (1991). Invariant Tori and Cylinders for a Class of Perturbed Hamiltonian Systems. In: Ratiu, T. (eds) The Geometry of Hamiltonian Systems. Mathematical Sciences Research Institute Publications, vol 22. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9725-0_13
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DOI: https://doi.org/10.1007/978-1-4613-9725-0_13
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