Perturbations of stable invariant tori for hamiltonian systems

L. H. Eliasson

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1988)

  • Volume: 15, Issue: 1, page 115-147
  • ISSN: 0391-173X

How to cite

top

Eliasson, L. H.. "Perturbations of stable invariant tori for hamiltonian systems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 15.1 (1988): 115-147. <http://eudml.org/doc/84022>.

@article{Eliasson1988,
author = {Eliasson, L. H.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {small divisor problem; stable invariant tori; stable tori; perturbations},
language = {eng},
number = {1},
pages = {115-147},
publisher = {Scuola normale superiore},
title = {Perturbations of stable invariant tori for hamiltonian systems},
url = {http://eudml.org/doc/84022},
volume = {15},
year = {1988},
}

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
PB - Scuola normale superiore
VL - 15
IS - 1
SP - 115
EP - 147
LA - eng
KW - small divisor problem; stable invariant tori; stable tori; perturbations
UR - http://eudml.org/doc/84022
ER -

References

top
  1. [1] V.I. Arnold, Mathematical methods of classical mechanics, Springer (1978). Zbl0386.70001MR690288
  2. [2] J. Vey, Sur certains systèmes dynamiques séparables, American Journal of Mathematics, 100 (1978), pp. 591-614. Zbl0384.58012MR501141
  3. [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. [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. Zbl0129.16606MR163025
  5. [5] J. Moser, On the theory of quasiperiodic motions, Siam Review8 (1966), pp. 145-172. Zbl0243.34081MR203160
  6. [6] J. Moser, Convergent series expansions for quasiperiodic motions, Mathematische Annalen, 169 (1967), pp. 136-176. Zbl0149.29903MR208078
  7. [7] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, vol. I, Paris (1892). JFM30.0834.08
  8. [8] S. Graff, On the conservation of hyperbolic invariant tori for Hamiltonian systems, Journal of Differential Equations, 15 (1974), pp. 1-69. Zbl0257.34048MR365626
  9. [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. Zbl0334.58009MR426055
  10. [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. Zbl0143.11801
  11. [11] V.K. Melnikov, A family of conditionally periodic solutions of a Hamiltonian system, Soviet Mathematics Doklady, 9 (1968), No. 4, pp. 882-885. Zbl0185.17101
  12. [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. Zbl0533.34023MR743943
  13. [13] C.L. Charlier, Die Mechanik des Himmels, vol. 2, Leipzig (1907). Zbl38.0949.11JFM38.0949.11
  14. [14] A.S. Pyartli, Diophantine approximation on submanifolds of euclidean space, Functional Analysis and its Applications, 3 (1969), pp. 303-306. Zbl0216.04401
  15. [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. Zbl0319.35017MR467824
  16. [16] C.L. Siegel - J. Moser, Lectures on celestial mechanics, Springer (1971). Zbl0312.70017MR502448

Citations in EuDML Documents

top
  1. Raphaël Krikorian, Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compacts
  2. Wei-Min Wang, Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations
  3. Ricardo Pérez-Marco, KAM techniques in PDE
  4. Massimiliano Berti, Quasi-periodic solutions of Hamiltonian PDEs
  5. Massimiliano Berti, Quasi-periodic solutions of PDEs
  6. Jürgen Pöschel, A KAM-theorem for some nonlinear partial differential equations
  7. P. Duclos, P. Šťovíček, M. Vittot, Perturbation of an eigen-value from a dense point spectrum : a general Floquet hamiltonian
  8. Laurent Stolovitch, A KAM phenomenon for singular holomorphic vector fields
  9. Mario Ponce, Sur la persistance des courbes invariantes pour les dynamiques holomorphes fibrées lisses
  10. Massimiliano Berti, Luca Biasco, Enrico Valdinoci, Periodic orbits close to elliptic tori and applications to the three-body problem

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.