Citation: |
[1] |
G. Benettin, F. Fassò and M. Guzzo, Nekhoroshev-stability of $L_4$ and $L_5$ in the spatial restricted three-body problem, Regul. Chaotic Dyn., 3 (1998), 56-71. |
[2] |
A. D. Bryuno, Formal stability of Hamiltonian systems, Mat. Zametki, 1 (1967), 325-330; English translation, Math. Notes, 1 (1967), 216-219. |
[3] |
H. E. Cabral and K. R. Meyer, Stability of equilibria and fixed points of conservative systems, Nonlinearity, 12 (1999), 1351-1362.doi: 10.1088/0951-7715/12/5/309. |
[4] |
T. M. Cherry, On periodic solutions of Hamiltonian systems of differential equations, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 227 (1928), 137-221.doi: 10.1098/rsta.1928.0005. |
[5] |
N. G. Chetaev, Un théorème sur l'instabilité, Dokl. Akad. Nauk SSSR, 1 (1934), 529-531. |
[6] |
G. L. Dirichlet, Über die stabilität des Gleichgewichts, J. Reine Angew. Math., 32 (1846), 85-88.doi: 10.1515/crll.1846.32.85. |
[7] |
F. Fassò and D. Lewis, Stability properties of the Riemann ellipsoids, Arch. Ration. Mech. Anal., 158 (2001), 259-292.doi: 10.1007/PL00004245. |
[8] |
A. Giorgilli, A. Delshams, E. Fontich, L. Galgani and C. Simó, Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem, J. Differential Equations, 77 (1989), 167-198.doi: 10.1016/0022-0396(89)90161-7. |
[9] |
J. Glimm, Formal stability of Hamiltonian systems, Comm. Pure Appl. Math., 16 (1963), 509-526. |
[10] |
L. G. Khazin, On the stability of Hamiltonian systems in the presence of resonances, Prikl. Mat. Mekh., 35 (1971), 423-431; English translation, J. Appl. Math. Mech., 35 (1971), 384-391. |
[11] |
A. L. Kunitsyn and A. A. Tuyakbayev, The stability of Hamiltonian systems in the case of a multiple fourth-order resonance, Prikl. Mat. Mekh., 56 (1992), 672-675; English translation, J. Appl. Math. Mech., 56 (1992), 572-576. |
[12] |
A. Liapounoff, Problème général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse, 9 (1907), 203-474; French translation of the 1892 Russian article. |
[13] |
K. R. Meyer, Normal forms for Hamiltonian systems, Celestial Mech., 9 (1974), 517-522. |
[14] |
K. R. Meyer, G. R. Hall and D. Offin, "Introduction to Hamiltonian Dynamical Systems and the $N$-Body Problem," $2^{nd}$ edition, Springer-Verlag, New York, 2009. |
[15] |
J. Moser, Stabilitätsverhalten kanonischer Differential gleichungs systeme, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa, 6 (1955), 87-120. |
[16] |
J. Moser, New aspects in the theory of stability of Hamiltonian systems, Comm. Pure Appl. Math., 11 (1958), 81-114.doi: 10.1002/cpa.3160110105. |
[17] |
J. Moser, On the elimination of the irrationality condition and Birkhoff's concept of complete stability, Bol. Soc. Mat. Mexicana (2), 5 (1960), 167-175. |
[18] |
J. Moser, Periodic orbits near an equilibrium and a theorem by Alan Weinstein, Comm. Pure Appl. Math., 29 (1976), 727-747; addendum in: Comm. Pure Appl. Math., 31 (1978), 529-530.doi: 10.1002/cpa.3160290613. |
[19] |
F. dos Santos, J. E. Mansilla and C. Vidal, Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems with $n$-degrees of freedom in the case of single resonance, J. Dynam. Differential Equations, 22 (2010), 805-821.doi: 10.1007/s10884-010-9176-z. |
[20] |
C. L. Siegel, Über die Existenz einer Normalform analytischer Hamiltonscher Differential gleichungen in der Nähe einer Gleichgewichtslösung, Math. Ann., 128 (1954), 144-170.doi: 10.1007/BF01360131. |
[21] |
V. G. Szebehely, "Theory of Orbits: The Restricted Problem of Three Bodies," Academic Press, New York, 1967. |
[22] |
C. Vidal, Stability of equilibrium positions of Hamiltonian systems, Qual. Theory Dyn. Syst., 7 (2008), 253-294. |
[23] |
A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math., 20 (1973), 47-57.doi: 10.1007/BF01405263. |
[24] |
A. Weinstein, Symplectic $V$-manifolds, periodic orbits of Hamiltonian systems, and the volume of certain Riemannian manifolds, Comm. Pure Appl. Math., 30 (1977), 265-271.doi: 10.1002/cpa.3160300207. |
[25] |
A. Weinstein, Bifurcations and Hamilton's principle, Math. Z., 159 (1978), 235-248.doi: 10.1007/BF01214573. |
[26] |
V. A. Yakubovich and V. M. Starzhinskii, "Linear Differential Equations with Periodic Coefficients," Vol. 1 and 2, John Wiley & Sons, New York, 1975. |