Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point

 Access to full text

 Full (PDF)

1. [1] G.D. Birkhoff, Dynamical systems, New York, 1927. Zbl53.0732.01JFM53.0732.01
2. [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. Zbl46.1173.02JFM46.1173.02
3. E.T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, London, 1970, p. 432 ff. 
4. [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. Zbl50.0305.01JFM50.0305.01
5. 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. Zbl51.0333.02JFM51.0333.02
6. [4] F.G. Gustavson, On constructing formal integrals of a Hamiltonian system near an equilibrium point. Astron. J., t. 71, 1966, p. 670-686. 
7. J.K. Moser, Lectures on Hamiltonian systems. Mem. Amer. Math. Soc., t. 81, 1968, p. 11 ff. Zbl0172.11401MR230498
8. [5] G. Contopoulos, A third integral of motion in a Galaxy. Z. Astrophys., t. 49, 1960, p. 273-291. Zbl0099.45007MR114635
9. G. Contopoulos, Resonant case and small divisors in a third integral of motion. I. Astron. J., t. 68, 1963, p. 763-779. MR158747
10. G. Contopoulos, Resonant case and small divisors in a third integral of motion, II. Astron. J., t. 70, 1965, p. 817-835. 
11. [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. Zbl0362.70024MR369777
12. [7] C.L. Siegel, On the integrals of canonical systems. Ann. Math., t. 42, 1941, p. 806-822. Zbl0025.26503MR5818
13. [8] J. Moser, Stabilitätsverhalten kanonisher differentialgleichungssysteme. Nachr. Akad. Wiss. Göttingen, Math. Phys. K1 IIa, nr., t. 6, 1955, p. 87-120. Zbl0066.33901MR79168
14. [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. Zbl0389.70028
15. 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). Zbl0668.34046
16. 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. Zbl0602.58022MR830795
17. G. Benettin and G. Gallavotti, Stability of motion near resonances in quasi integrable Hamiltonian systems. J. Stat. Phys., t. 44, 1986, p. 293-338. Zbl0636.70018MR857061
18. G. Gallavotti, Quasi-integrable mechanical systems, in K. Osterwalder and R. Stora (eds.). Les Houches, Session XLIII, 1984. Zbl0662.70022
19. [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. Zbl0675.70027
20. A. Giorgilli, L. Galgani, Rigorous estimates for the series expansions of Hamiltonian perturbation theory. Cel. Mech., t. 37, 1985, p. 95-112. MR838181
21. [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. Zbl0319.35017MR467824
22. [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. Zbl0387.70022MR504624

1. Giancarlo Benettin, Applicazioni del teorema di Nekhoroshev alla meccanica celeste