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, Volume 48 (1988) no. 4, pp. 423-439.
@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},
     pages = {423--439},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {4},
     year = {1988},
     mrnumber = {969174},
     zbl = {0669.34002},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1988__48_4_423_0/}
}
TY  - JOUR
AU  - Giorgilli, Antonio
TI  - Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1988
SP  - 423
EP  - 439
VL  - 48
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1988__48_4_423_0/
LA  - en
ID  - AIHPA_1988__48_4_423_0
ER  - 
%0 Journal Article
%A Giorgilli, Antonio
%T Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point
%J Annales de l'I.H.P. Physique théorique
%D 1988
%P 423-439
%V 48
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1988__48_4_423_0/
%G en
%F 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, Volume 48 (1988) no. 4, pp. 423-439. http://archive.numdam.org/item/AIHPA_1988__48_4_423_0/

[1] G.D. Birkhoff, Dynamical systems, New York, 1927. | JFM

[2] E.T. Whittaker, On the adelphic integral of the differential equations of dynamics. Proc. Roy Soc. Edinburgh, Sect. A, t. 37, 1916, p. 95-109. | JFM

E.T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, London, 1970, p. 432 ff.

[3] T.M. Cherry, 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

T.M. Cherry, 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

[4] F.G. Gustavson, On constructing formal integrals of a Hamiltonian system near an equilibrium point. Astron. J., t. 71, 1966, p. 670-686.

J.K. Moser, Lectures on Hamiltonian systems. Mem. Amer. Math. Soc., t. 81, 1968, p. 11 ff. | MR | Zbl

[5] G. Contopoulos, A third integral of motion in a Galaxy. Z. Astrophys., t. 49, 1960, p. 273-291. | MR | Zbl

G. Contopoulos, Resonant case and small divisors in a third integral of motion. I. Astron. J., t. 68, 1963, p. 763-779. | MR

G. Contopoulos, Resonant case and small divisors in a third integral of motion, II. Astron. J., t. 70, 1965, p. 817-835.

[6] E. Diana, L. Galgani, A. Giorgilli and A. Scotti, 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 | Zbl

[7] C.L. Siegel, On the integrals of canonical systems. Ann. Math., t. 42, 1941, p. 806-822. | JFM | MR | Zbl

[8] J. Moser, Stabilitätsverhalten kanonisher differentialgleichungssysteme. Nachr. Akad. Wiss. Göttingen, Math. Phys. K1 IIa, nr., t. 6, 1955, p. 87-120. | MR | Zbl

[9] N.N. Nekhoroshev, Exponential estimate of the stability time of near-integrable Hamiltonian systems. Russ. Math. Surveys, t. 32, n° 6, 1977, p. 1-65. | Zbl

N.N. Nekhoroshev, Exponential estimate of the stability time of near-integrable Hamiltonian systems, II. Trudy Sem. Petrovs., n° 5, 1979, p. 5-50 (in russian). | Zbl

G. Benettin, L. Galgani and A. Giorgilli, A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltoniar systems. Cel. Mech., t. 37, 1985, p. 1-25. | MR | Zbl

G. Benettin and G. Gallavotti, Stability of motion near resonances in quasi integrable Hamiltonian systems. J. Stat. Phys., t. 44, 1986, p. 293-338. | MR | Zbl

G. Gallavotti, Quasi-integrable mechanical systems, in K. Osterwalder and R. Stora (eds.). Les Houches, Session XLIII, 1984. | Zbl

[10] 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 be restricted three body problem. J. Diff. Eqs., to appear. | Zbl

A. Giorgilli, L. Galgani, Rigorous estimates for the series expansions of Hamiltonian perturbation theory. Cel. Mech., t. 37, 1985, p. 95-112. | MR

[11] H. Russman, 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 | Zbl

[12] A. Giorgilli and L. Galgani, Formal integrals for an autonomous Hamiltonian system near an equilibrium point. Cel. Mech., t. 17, 1978, p. 267-280. | MR | Zbl