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Planetary Birkhoff normal forms
1. | Dipartimento di Matematica, Università "Roma Tre", Largo S. L. Murialdo 1, 00146 Roma |
2. | Dipartimento di Matematica, Università “Roma Tre”, Largo S. L. Murialdo 1, I-00146 Roma, Italy |
References:
[1] |
K. Abdullah and A. Albouy, On a strange resonance noticed by M. Herman, Regul. Chaotic Dyn., 6 (2001), 421-432.
doi: 10.1070/RD2001v006n04ABEH000186. |
[2] |
V. I. Arnol'd, Small denominators and problems of stability of motion in classical and celestial mechanics, Uspehi Mat. Nauk, 18 (1963), 91-192. |
[3] |
L. Biasco, L. Chierchia and E. Valdinoci, Elliptic two-dimensional invariant tori for the planetary three-body problem, Arch. Rational Mech. Anal., 170 (2003), 91-135. See also Corrigendum, Arch. Ration. Mech. Anal., 180 (2006), 507-509.
doi: 10.1007/s00205-005-0410-5. |
[4] |
L. Chierchia and G. Pinzari, Properly-degenerate KAM theory (following V. I. Arnold), Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 545-578.
doi: 10.3934/dcdss.2010.3.545. |
[5] |
L. Chierchia and G. Pinzari, Deprit's reduction of the nodes revisited, Celestial Mech. Dynam. Astronom., 109 (2011), 285-301.
doi: 10.1007/s10569-010-9329-8. |
[6] |
L. Chierchia and G. Pinzari, The planetary N-body problem: Symplectic foliation, reductions and invariant tori, Invent. Math., 186 (2011), 1-77.
doi: 10.1007/s00222-011-0313-z. |
[7] |
L. Chierchia and F. Pusateri, Analytic Lagrangian tori for the planetary many-body problem, Ergodic Theory Dynam. Systems, 29 (2009), 849-873.
doi: 10.1017/S0143385708000503. |
[8] |
A. Deprit, Elimination of the nodes in problems of $n$ bodies, Celestial Mech., 30 (1983), 181-195.
doi: 10.1007/BF01234305. |
[9] |
J. Féjoz, Quasiperiodic motions in the planar three-body problem, J. Differential Equations, 183 (2002), 303-341.
doi: 10.1006/jdeq.2001.4117. |
[10] |
J. Féjoz, Démonstration du 'théorème d'Arnold' sur la stabilité du système planétaire (d'après Herman), Ergodic Theory Dynam. Systems, 24 (2004), 1521-1582. |
[11] |
M. R. Herman, Torsion du problème planètaire, ed. J. Fejóz, 'Archives Michel Herman', 2009. Available from: http://www.college-de-france.fr/default/EN/all/equ_dif/archives_michel_herman.htm. |
[12] |
H. Hofer and E. Zehnder, "Symplectic Invariants and Hamiltonian Dynamics," Birkhäuser Verlag, Basel, 1994.
doi: 10.1007/978-3-0348-8540-9. |
[13] |
N. N. Nehorošev, An exponential estimate of the time of stability of nearly integrable Hamiltonian systems, Uspehi Mat. Nauk, 32 (1977), 5-66, 287. |
[14] |
L. Niederman, Stability over exponentially long times in the planetary problem, Nonlinearity, 9 (1996), 1703-1751.
doi: 10.1088/0951-7715/9/6/017. |
[15] |
J. Pöschel, Nekhoroshev estimates for quasi-convex Hamiltonian systems, Math. Z., 213 (1993), 187-216.
doi: 10.1007/BF03025718. |
[16] |
P. Robutel, Stability of the planetary three-body problem. II. KAM theory and existence of quasiperiodic motions, Celestial Mech. Dynam. Astronom., 62 (1995), 219-261. See also Erratum, Celestial Mech. Dynam. Astronom., 84 (2002), 317.
doi: 10.1023/A:1020355823815. |
show all references
References:
[1] |
K. Abdullah and A. Albouy, On a strange resonance noticed by M. Herman, Regul. Chaotic Dyn., 6 (2001), 421-432.
doi: 10.1070/RD2001v006n04ABEH000186. |
[2] |
V. I. Arnol'd, Small denominators and problems of stability of motion in classical and celestial mechanics, Uspehi Mat. Nauk, 18 (1963), 91-192. |
[3] |
L. Biasco, L. Chierchia and E. Valdinoci, Elliptic two-dimensional invariant tori for the planetary three-body problem, Arch. Rational Mech. Anal., 170 (2003), 91-135. See also Corrigendum, Arch. Ration. Mech. Anal., 180 (2006), 507-509.
doi: 10.1007/s00205-005-0410-5. |
[4] |
L. Chierchia and G. Pinzari, Properly-degenerate KAM theory (following V. I. Arnold), Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 545-578.
doi: 10.3934/dcdss.2010.3.545. |
[5] |
L. Chierchia and G. Pinzari, Deprit's reduction of the nodes revisited, Celestial Mech. Dynam. Astronom., 109 (2011), 285-301.
doi: 10.1007/s10569-010-9329-8. |
[6] |
L. Chierchia and G. Pinzari, The planetary N-body problem: Symplectic foliation, reductions and invariant tori, Invent. Math., 186 (2011), 1-77.
doi: 10.1007/s00222-011-0313-z. |
[7] |
L. Chierchia and F. Pusateri, Analytic Lagrangian tori for the planetary many-body problem, Ergodic Theory Dynam. Systems, 29 (2009), 849-873.
doi: 10.1017/S0143385708000503. |
[8] |
A. Deprit, Elimination of the nodes in problems of $n$ bodies, Celestial Mech., 30 (1983), 181-195.
doi: 10.1007/BF01234305. |
[9] |
J. Féjoz, Quasiperiodic motions in the planar three-body problem, J. Differential Equations, 183 (2002), 303-341.
doi: 10.1006/jdeq.2001.4117. |
[10] |
J. Féjoz, Démonstration du 'théorème d'Arnold' sur la stabilité du système planétaire (d'après Herman), Ergodic Theory Dynam. Systems, 24 (2004), 1521-1582. |
[11] |
M. R. Herman, Torsion du problème planètaire, ed. J. Fejóz, 'Archives Michel Herman', 2009. Available from: http://www.college-de-france.fr/default/EN/all/equ_dif/archives_michel_herman.htm. |
[12] |
H. Hofer and E. Zehnder, "Symplectic Invariants and Hamiltonian Dynamics," Birkhäuser Verlag, Basel, 1994.
doi: 10.1007/978-3-0348-8540-9. |
[13] |
N. N. Nehorošev, An exponential estimate of the time of stability of nearly integrable Hamiltonian systems, Uspehi Mat. Nauk, 32 (1977), 5-66, 287. |
[14] |
L. Niederman, Stability over exponentially long times in the planetary problem, Nonlinearity, 9 (1996), 1703-1751.
doi: 10.1088/0951-7715/9/6/017. |
[15] |
J. Pöschel, Nekhoroshev estimates for quasi-convex Hamiltonian systems, Math. Z., 213 (1993), 187-216.
doi: 10.1007/BF03025718. |
[16] |
P. Robutel, Stability of the planetary three-body problem. II. KAM theory and existence of quasiperiodic motions, Celestial Mech. Dynam. Astronom., 62 (1995), 219-261. See also Erratum, Celestial Mech. Dynam. Astronom., 84 (2002), 317.
doi: 10.1023/A:1020355823815. |
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