Sur la non-intégrabilité de potentiels quartiques

Olivier Vivolo

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 3, page 535-556
  • ISSN: 0240-2963

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Vivolo, Olivier. "Sur la non-intégrabilité de potentiels quartiques." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.3 (1997): 535-556. <http://eudml.org/doc/73433>.

@article{Vivolo1997,
author = {Vivolo, Olivier},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Hénon-Heiles system; non-integrability of Hamiltonian systems; Ziglin theorem},
language = {fre},
number = {3},
pages = {535-556},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Sur la non-intégrabilité de potentiels quartiques},
url = {http://eudml.org/doc/73433},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Vivolo, Olivier
TI - Sur la non-intégrabilité de potentiels quartiques
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 3
SP - 535
EP - 556
LA - fre
KW - Hénon-Heiles system; non-integrability of Hamiltonian systems; Ziglin theorem
UR - http://eudml.org/doc/73433
ER -

References

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  2. [AS] Aisawa ( Y.) et Saitô ( N.) .— On the stability of isolating integrals: I effect of the perturbation in the potential function, J. Phys. Soc., Japon, 32 (1972), pp. 1636-1640. 
  3. [BSV] Bountis ( T.), Segur ( H.) et Vivaldi ( F.) .— Integrable Hamiltonian systems and the Painlevé Property, J. Phys. Rev. A25 (1982), pp. 1257-1264. MR647746
  4. [Ba] Bateman ( H.) et Erdelyi ( A.) .— Higher Transcendental Functions, McGraw-HillNew-York (1955). Zbl0052.29502MR66496
  5. [CTW] Chang ( Y.F.), Tabor ( M.) et Weiss ( J.) .— Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes, J. Math. Phys.23 (1982), pp. 513-538. Zbl0492.70019MR649531
  6. [GDP] Grammaticos ( B.), Dorizzi ( B.) et Padjen ( R.) .— Painlevé property and integrals of motion for the Henon-Heiles system, Phys. Lett. A89 (1982), pp. 111-113. MR658270
  7. [HH] Henon ( M.) et Heiles ( C.) . — The Applicability of the third integral of motion: some numerical experiments, Astrophys.63 (1964), pp. 73-78. MR158746
  8. [It] Ito ( H.) .— Non Integrablity of Hénon-Heiles System and a Theorem of Ziglin, Kodai Math. J8 (1985), pp. 120-138. Zbl0577.58016MR776713
  9. [Li] Lindstëdt ( A.) .— Mémoire de l'Académie de Saint-Pétersbourg, (1882). 
  10. [P1] Poincaré ( H.) .— Sur une méthode de M. Lindstëdt, Bulletin Astronomique Tome III (1886), p. 57. 
  11. [P2] Poincaré ( H.) .— Les méthodes nouvelles de la mécanique céleste, Tome II, Dover Publi.New-York, 1957 (chap. IX et XIII). 
  12. [Ra] Ravoson ( V.) . — (r, s)-Structure bi-hamiltonienne, séparabilité, paires de Lax et intégrabilité, Thèse, Université de Pau et des Pays de l'Adour (1992). 
  13. [Zi] Ziglin ( S.L.) . — Branching of Solutions and Non-existence of First Integrals in Hamiltonian Mechanics, Funct. Anal. Appl.16 (1983), pp. 181-169; Funct. Anal. Appl.17 (1983), pp. 6-17. Zbl0518.58016

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