Perturbations of stable invariant tori for hamiltonian systems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 15 (1988) no. 1, pp. 115-147.
@article{ASNSP_1988_4_15_1_115_0,
     author = {Eliasson, L. H.},
     title = {Perturbations of stable invariant tori for hamiltonian systems},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {115--147},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 15},
     number = {1},
     year = {1988},
     zbl = {0685.58024},
     mrnumber = {1001032},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1988_4_15_1_115_0/}
}
TY  - JOUR
AU  - Eliasson, L. H.
TI  - Perturbations of stable invariant tori for hamiltonian systems
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1988
DA  - 1988///
SP  - 115
EP  - 147
VL  - Ser. 4, 15
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1988_4_15_1_115_0/
UR  - https://zbmath.org/?q=an%3A0685.58024
UR  - https://www.ams.org/mathscinet-getitem?mr=1001032
LA  - en
ID  - ASNSP_1988_4_15_1_115_0
ER  - 
%0 Journal Article
%A Eliasson, L. H.
%T Perturbations of stable invariant tori for hamiltonian systems
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1988
%P 115-147
%V Ser. 4, 15
%N 1
%I Scuola normale superiore
%G en
%F ASNSP_1988_4_15_1_115_0
Eliasson, L. H. Perturbations of stable invariant tori for hamiltonian systems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 15 (1988) no. 1, pp. 115-147. http://archive.numdam.org/item/ASNSP_1988_4_15_1_115_0/

[1] V.I. Arnold, Mathematical methods of classical mechanics, Springer (1978). | MR | Zbl

[2] J. Vey, Sur certains systèmes dynamiques séparables, American Journal of Mathematics, 100 (1978), pp. 591-614. | MR | Zbl

[3] A.N. Kolmogorov, The general theory of dynamical systems and classical mechanics, Proc. of the 1954 Intern. Congr. of Math., in R. Abraham, J.E. Marsden, Foundations of mechanics, Benjamin (1978).

[4] V.I. Arnold, Proof of a theorem of A.N. Kolmogorov on the invariance of quasiperiodic motions under small perturbations of the Hamiltonian, Russian Mathematical Surveys, 18 (1962), No. 5, pp. 9-36. | MR | Zbl

[5] J. Moser, On the theory of quasiperiodic motions, Siam Review 8 (1966), pp. 145-172. | MR | Zbl

[6] J. Moser, Convergent series expansions for quasiperiodic motions, Mathematische Annalen, 169 (1967), pp. 136-176. | MR | Zbl

[7] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, vol. I, Paris (1892). | JFM

[8] S. Graff, On the conservation of hyperbolic invariant tori for Hamiltonian systems, Journal of Differential Equations, 15 (1974), pp. 1-69. | MR | Zbl

[9] E. Zehnder, Generalized implicit function theorems with application to some small divisor problems II, Communications on Pure and Applied Mathematics, 29 (1976), pp. 49-111. | MR | Zbl

[10] V.K. Melnikov, On some cases of conservation of conditionally periodic motions under a small change of the Hamiltonian function, Soviet Mathematics Doklady, 6 (1965), pp. 1592-1596. | Zbl

[11] V.K. Melnikov, A family of conditionally periodic solutions of a Hamiltonian system, Soviet Mathematics Doklady, 9 (1968), No. 4, pp. 882-885. | Zbl

[12] J. Moser - J. Pöschel, An extension of a result by Dinaburg and Sinai on quasiperiodic potentials, Commentarii Mathematici Helvetici, 59 (1984), pp. 39-85. | MR | Zbl

[13] C.L. Charlier, Die Mechanik des Himmels, vol. 2, Leipzig (1907). | JFM

[14] A.S. Pyartli, Diophantine approximation on submanifolds of euclidean space, Functional Analysis and its Applications, 3 (1969), pp. 303-306. | Zbl

[15] H. Rüssmann, On optimal estimates for the solutions of linear partial differential equations of the first order with constant coefficients on the torus, Springer, Lecture Notes in Physics, Vol. 38 (1975), pp. 598-624. | MR | Zbl

[16] C.L. Siegel - J. Moser, Lectures on celestial mechanics, Springer (1971). | MR | Zbl