@article{AIHPA_1988__48_4_423_0,
author = {Giorgilli, Antonio},
title = {Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {49},
year = {1988},
pages = {423-439},
mrnumber = {969174},
zbl = {0669.34002},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1988__48_4_423_0}
}
Giorgilli, Antonio. Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point. Annales de l'I.H.P. Physique théorique, Tome 49 (1988) pp. 423-439. http://gdmltest.u-ga.fr/item/AIHPA_1988__48_4_423_0/
[1] , Dynamical systems, New York, 1927. | JFM 53.0732.01
[2] , On the adelphic integral of the differential equations of dynamics. Proc. Roy Soc. Edinburgh, Sect. A, t. 37, 1916, p. 95-109. | JFM 46.1173.02
, A treatise on the analytical dynamics of particles and rigid bodies, London, 1970, p. 432 ff.
[3] , On integrals developable about a singular point of a Hamiltonian system of differential equations. Proc. Camb. Phil. Soc., t. 22, 1924, p. 325-349. | JFM 50.0305.01
, On integrals developable about a singular point of a Hamiltonian system of differential equations. II. Proc. Camb. Phil. Soc., t. 22, 1924, p. 510-533. | JFM 51.0333.02
[4] , On constructing formal integrals of a Hamiltonian system near an equilibrium point. Astron. J., t. 71, 1966, p. 670-686.
, Lectures on Hamiltonian systems. Mem. Amer. Math. Soc., t. 81, 1968, p. 11 ff. | MR 230498 | Zbl 0172.11401
[5] , A third integral of motion in a Galaxy. Z. Astrophys., t. 49, 1960, p. 273-291. | MR 114635 | Zbl 0099.45007
, Resonant case and small divisors in a third integral of motion. I. Astron. J., t. 68, 1963, p. 763-779. | MR 158747
, Resonant case and small divisors in a third integral of motion, II. Astron. J., t. 70, 1965, p. 817-835.
[6] , , and , On the direct construction of formal integrals of a Hamiltonian system near an equilibrium point. Boll. Un. Mat. It., t. 11, 1975, p. 84-89. | MR 369777 | Zbl 0362.70024
[7] , On the integrals of canonical systems. Ann. Math., t. 42, 1941, p. 806-822. | JFM 67.0768.01 | MR 5818 | Zbl 0025.26503
[8] , Stabilitätsverhalten kanonisher differentialgleichungssysteme. Nachr. Akad. Wiss. Göttingen, Math. Phys. K1 IIa, nr., t. 6, 1955, p. 87-120. | MR 79168 | Zbl 0066.33901
[9] , Exponential estimate of the stability time of near-integrable Hamiltonian systems. Russ. Math. Surveys, t. 32, n° 6, 1977, p. 1-65. | Zbl 0389.70028
, Exponential estimate of the stability time of near-integrable Hamiltonian systems, II. Trudy Sem. Petrovs., n° 5, 1979, p. 5-50 (in russian). | Zbl 0473.34021 | Zbl 0668.34046
, and , A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltoniar systems. Cel. Mech., t. 37, 1985, p. 1-25. | MR 830795 | Zbl 0602.58022
and , Stability of motion near resonances in quasi integrable Hamiltonian systems. J. Stat. Phys., t. 44, 1986, p. 293-338. | MR 857061 | Zbl 0636.70018
, Quasi-integrable mechanical systems, in K. Osterwalder and R. Stora (eds.). Les Houches, Session XLIII, 1984. | Zbl 0662.70022
[10] , , , and , Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to be restricted three body problem. J. Diff. Eqs., to appear. | Zbl 0675.70027
, , Rigorous estimates for the series expansions of Hamiltonian perturbation theory. Cel. Mech., t. 37, 1985, p. 95-112. | MR 838181
[11] , On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus, in J. Ehlers, K. Hepp and H. A. Weidenmüller, eds., Dynamical systems, theory and applications. Lecture notes in Physics, t. 38, 1974, p. 598-624. | MR 467824 | Zbl 0319.35017
[12] and , Formal integrals for an autonomous Hamiltonian system near an equilibrium point. Cel. Mech., t. 17, 1978, p. 267-280. | MR 504624 | Zbl 0387.70022