Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems

Communications in Mathematical Physics

Volumn 197, Issue 2, 1998, Pages 347-360

  Fassò, Francesco ^a   Guzzo, Massimiliano ^a   Benettin, Giancarlo ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032187844     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050454     Document Type: Article

References (21)

1. Bambusi, D.: Long time stability of some small amplitude solutions in nonlinear Schřdinger equations. Commun. Math. Phys. 189, 205-226 (1997)
2. Benettin, G. and Gallavotti, G.: Stability of motions near resonances in quasi-integrable Hamiltonian systems. J. Stat. Phys. 44, 293-338 (1986)
3. Benettin, G., Fassò, F. and Guzzo, M.: Fast rotations of the rigid body: A study by Hamiltonian perturbation theory. Part II: Gyroscopic rotations. Nonlinearity 10, 1695-1717 (1997)
4. Chandrasekhar, S.: Ellipsoidal Figures of Equilibrium. New Haven, CT: Yale University Press, 1969
5. Delshams, A. and Gutiérrez, P.: Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system. J. Diff. Eq. 131, 277-303 (1996)
6. Fassò, F.: Lie series method for vector fields and Hamiltonian perturbation theory. J. Appl. Math. Phys. (ZAMP) 41, 843-864 (1990)
7. Fassò, F. and Lewis, D.: Paper in preparation
8. Gallavotti, G.: Quasi-Integrable Mechanical Systems. In: Critical phenomena, Random Systems, Gauge Theories, K. Osterwalder and R. Stora editors, Les Houches, Session XLIII, 1984 Amsterdam: North-Holland, 1986
9. Giorgilli, A. and Galgani, L.: Rigorous estimates for the series expansions of Hamiltonian perturbation theory. Celestial Mechanics 37, 95-112 (1985)
10. Giorgilli, A.: Rigorous results on the power expansions for the integrals of a Hamiltonian system near an elliptic equilibrium point. Ann. Inst. Henri Poincaré - Physique Thèorique 48, 423-439 (1988)
11. Giorgilli, A., Delshams, A., Fontich, E., Galgani, L. and Simó, C.: Effective Stability for a Hamiltonian System near an Elliptic Equilibrium Point, with an Application to the Restricted three Body Problem. J. Diff. Eq. 77, 167-198 (1989)
12. Guzzo, M., Fassò, F. and Benettin, G.: On the stability of elliptic equilibria. MPEJ - Mathematical Physics Electronic Journal 4, Paper 1 (1998)
13. Ito, H.: Convergence of Birkhoff normal forms for integrable systems. Comment. Math. Helvetici 64, 412-461 (1989)
14. Jorba, À. and Villanueva, J.: On the normal behaviour of partially elliptic lower dimensional tori of Hamiltonian systems. Nonlinearity 10, 783-822 (1997)
15. Lewis, D.: Bifurcation of liquid drops. Nonlinearity 6, 491-522 (1993)
16. Lochak, P.: Canonical perturbation theory via simultaneous approximation. Russ. Math. Surv. 47, 57-133 (1992)
17. Lochak, P.: Stability of Hamiltonian systems over exponentially long times: the near linear case. In: H. Dumas, K. Meyer, D. Schmidt (eds), Hamiltonian Dynamical Systems - History, Theory, and Applications, The IMA Volumes in Mathematics and its Applications 63, New York: Springer, 1995, pp. 221-229
18. Nekhoroshev, N.N.: An exponential estimate of the time of stability of nearly integrable Hamiltonian systems. Usp. Mat. Nauk 32:6, 5-66 (1977) [Russ. Math. Surv. 32:6, 1-65 (1977)]
19. Nekhoroshev, N.N.: An exponential estimate of the time of stability of nearly integrable Hamiltonian systems. Usp. Mat. Nauk 32:6, 5-66 (1977) [Russ. Math. Surv. 32:6, 1-65 (1977)]
20. Pöschel, J.: Nekhoroshev estimates for quasi-convex Hamiltonian Systems. Math. Z. 213, 187-216 (1993)
21. Siegel, C. and Moser, J.: Lectures on Celestial Mechanics. Berlin: Springer, 1971