On "Arnold's theorem" on the stability of the solar system
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K. Abdullah, 2001, <em>On a strange resonance noticed by M. Herman</em>,, Regul. Chaotic Dyn., 6, 421, 10.1070/RD2001v006n04ABEH000186
V. I. Arnold, 1963, <em>Small denominators and problems of stability of motion in classical and celestial mechanics</em>,, Uspehi Mat. Nauk, 18, 91
V. I. Arnold, 2006, "Mathematical Aspects Of Classical and Celestial Mechanics," Translated from the Russian original by E. Khukhro, Third edition, Encyclopaedia of Mathematical Sciences, <strong>3</strong>,, Springer-Verlag
A. Celletti, 2006, <em>KAM stability for a three-body problem of the solar system</em>,, Z. Angew. Math. Phys., 57, 33, 10.1007/s00033-005-0002-0
A. Celletti, 2007, <em>KAM stability and celestial mechanics</em>,, Mem. Amer. Math. Soc., 187
A. Chenciner, 1989, <em>Intégration du problème de Kepler par la méthode de Hamilton-Jacobi</em>,, Technical report
L. Chierchia, 2010, <em>Properly-degenerate KAM theory (following V. I. Arnold)</em>,, Discrete Contin. Dyn. Syst. Ser. S, 3, 545, 10.3934/dcdss.2010.3.545
L. Chierchia, 2011, <em>Planetary Birkhoff normal forms</em>,, J. Mod. Dyn., 5, 623, 10.3934/jmd.2011.5.623
L. Chierchia, 2011, <em>The planetary $N$-body problem: Symplectic foliation, reductions and invariant tori</em>,, Invent. Math., 186, 1, 10.1007/s00222-011-0313-z
J. Féjoz, 2004, <em>Démonstration du 'théorème d'Arnold' sur la stabilité du système planétaire (d'après Herman)</em>,, Ergodic Theory Dynam. Systems, 24, 1521, 10.1017/S0143385704000410
J. Féjoz, 2011, <em>Diffusion along mean motion resonance in the restricted planar three-body problem</em>,, preprint
J. Galante, 2011, <em>Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action</em>,, Duke Math. J., 159, 275, 10.1215/00127094-1415878
M. Hénon, 1966, <em>Exploration numérique du problème restreint IV. masses égales, orbites non périodiques</em>,, Bulletin Astronomique, 3, 49
A. N. Kolmogorov, 1954, <em>On the conservation of conditionally periodic motions for a small change in Hamilton's function</em>,, Dokl. Akad. Nauk SSSR (N.S.), 98, 527
J. Laskar, 1990, <em>The chaotic motion of the solar system. a numerical estimate of the size of the chaotic zones</em>,, Icarus, 88, 266, 10.1016/0019-1035(90)90084-M
J. Laskar, 2010, <em>Le système solaire est-il stable?</em>,, in, XIV, 221
J. Laskar, 1995, <em>Stability of the planetary three-body problem. I. Expansion of the planetary Hamiltonian</em>,, Celestial Mech. Dynam. Astronom., 62, 193, 10.1007/BF00692088
M. L. Lidov, 1976, <em>Non-restricted double-averaged three body problem in Hill's case</em>,, Celestial Mech., 13, 471, 10.1007/BF01229100
U. Locatelli, 2007, <em>Invariant tori in the Sun-Jupiter-Saturn system</em>,, Discrete Contin. Dyn. Syst. Ser. B, 7, 377, 10.3934/dcdsb.2007.7.377
F. Malige, 2002, <em>Partial reduction in the n-body planetary problem using the angular momentum integral</em>,, Celestial Mechanics and Dynamical Astronomy, 84, 283, 10.1023/A:1020392219443
R. Moeckel, 1988, <em>Some qualitative features of the three-body problem</em>,, in, 81, 1, 10.1090/conm/081/986254
A. Moltchanov, 1968, <em>The resonant structure of the solar system</em>,, Icarus, 8, 203, 10.1016/0019-1035(68)90074-2
J. Moser, 1973, "Stable and Random Motions in Dynamical Systems,", With special emphasis on celestial mechanics
J. Moser, 2005, "Notes on Dynamical Systems," Courant Lecture Notes in Mathematics, <strong>12</strong>,, New York University
N. N. Nehorošev, 1979, <em>An exponential estimate of the time of stability of nearly integrable Hamiltonian systems. II</em>,, Trudy Sem. Petrovsk., 5, 5
A. Neishtadt, 2003, <em>On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations</em>,, Dedicated to V. I. Arnold on the occasion of his 65th birthday, 3, 1039
A. Neishtadt, 2008, <em>Averaging method and adiabatic invariants</em>,, in, 53, 10.1007/978-1-4020-6964-2_3
L. Niederman, 1996, <em>Stability over exponentially long times in the planetary problem</em>,, Nonlinearity, 9, 1703, 10.1088/0951-7715/9/6/017
G. Pinzari, 2009, "On the Kolmogorov Set for Many-Body Problems,", Ph.D thesis
H. Poincaré, 1892, "Les Méthodes Nouvelles de la Mécanique Céleste. Tome I, Solutions Périodiques. Non-Existence des Intégrales Uniformes. Solutions Asymptotiques,", Librairie Scientifique et Technique Albert Blanchard
H. Poincaré, 1905, "Leçons de Mécanique Céleste,", Gauthier-Villars
A. S. Pyartli, 1969, <em>Diophantine approximations of submanifolds of a Euclidean space</em>,, Funkcional. Anal. i Priložen., 3, 59
P. Robutel, 1995, <em>Stability of the planetary three-body problem. II. KAM theory and existence of quasiperiodic motions</em>,, Celestial Mech. Dynam. Astronom., 62, 219, 10.1007/BF00692089
C. Simó, 2000, <em>Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem</em>,, Phys. D, 140, 1, 10.1016/S0167-2789(99)00211-0
E. L. Stiefel, 1971, "Linear and Regular Celestial Mechanics. Perturbed Two-Body Motion, Numerical Methods, Canonical Theory,", Die Grundlehren der mathematischen Wissenschaften
F. Tisserand, 1896, "Traité de Mécanique Céleste,", Gauthier-Villars