On a galoisian approach to the splitting of separatrices

Juan J. Morales-Ruiz; Josep Maria Peris

Annales de la Faculté des sciences de Toulouse : Mathématiques (1999)

  • Volume: 8, Issue: 1, page 125-141
  • ISSN: 0240-2963

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Morales-Ruiz, Juan J., and Maria Peris, Josep. "On a galoisian approach to the splitting of separatrices." Annales de la Faculté des sciences de Toulouse : Mathématiques 8.1 (1999): 125-141. <http://eudml.org/doc/73474>.

@article{Morales1999,
author = {Morales-Ruiz, Juan J., Maria Peris, Josep},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Hamiltonian systems; homoclinic orbit; Ziglin nonintegrability theorem; Lerman theorem; Galois differential approach},
language = {eng},
number = {1},
pages = {125-141},
publisher = {UNIVERSITE PAUL SABATIER},
title = {On a galoisian approach to the splitting of separatrices},
url = {http://eudml.org/doc/73474},
volume = {8},
year = {1999},
}

TY - JOUR
AU - Morales-Ruiz, Juan J.
AU - Maria Peris, Josep
TI - On a galoisian approach to the splitting of separatrices
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1999
PB - UNIVERSITE PAUL SABATIER
VL - 8
IS - 1
SP - 125
EP - 141
LA - eng
KW - Hamiltonian systems; homoclinic orbit; Ziglin nonintegrability theorem; Lerman theorem; Galois differential approach
UR - http://eudml.org/doc/73474
ER -

References

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  2. [2] . Churchill ( R.C.), Rod ( D.L.). — On the determination of Ziglin monodromy Groups, S.I.A.M. J. Math. Anal.22 (1991), pp. 1790-1802. Zbl0739.58018MR1129412
  3. [3] Churchill ( R.C.), Rod ( D.L.) and Sleeman ( B.D.) .— Symmetric Connections and the Geometry of Doubly-Periodic Floquet Theory, Preprint 1996. 
  4. [4] Grotta-Ragazzo ( C.) . - Nonintegrability of some Hamiltonian Systems, Scattering and Analytic Continuation, Commun. Math. Phys.166 (1994), pp. 255-277. Zbl0814.70009MR1309550
  5. [5] Kaplansky ( I.) .— An Introduction to Differential Algebra, Hermann1976. MR460303
  6. [6] Katz ( N.M.) . — A conjecture in the arithmetic theory of differential equations, Bull. Soc. Math. France110 (1982), pp. 203-239. Zbl0504.12022MR667751
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  8. [8] Kovacic ( J.J.) . - An Algorithm for Solving Second Order Linear Homogeneous Differential Equations, J. Symb. Comput.2, (1986), pp. 3-43. Zbl0603.68035MR839134
  9. [9] Lerman ( L.M.) .— Hamiltonian systems with loops of a separatrix of a saddlecenter, Sel. Math. Sov.10 (1991), pp. 297-306. Zbl0743.58017MR1120110
  10. [10] Martinet ( J.) and Ramis ( J.-P.) .- Théorie de Galois différentielle et resommation, Computer Algebra and Differential Equations, E. Tournier Ed., Academic Press1989, pp. 117-214. Zbl0722.12007MR1038060
  11. [11] Morales-Ruiz ( J.J.) and Ramis ( J.-P.) .- Galoisian obstructions to integrability of Hamiltonian systems, In preparation. Zbl1140.37354
  12. [12] Morales-Ruiz ( J.J.) and Simó ( C.) .— Picard—Vessiot Theory and Ziglin's Theorem, J. Diff. Eq.107 (1994), pp. 140-162. Zbl0799.58035MR1260852
  13. [13] Morales-Ruiz ( J.J.) and Simó ( C.) . - Non integrability criteria for Hamiltonians in the case of Lamé Normal Variational Equations, J. Diff. Eq.129 (1996), pp. 111-135. Zbl0866.58034MR1400798
  14. [14] Poole ( E.G.C.) .- Introduction to the theory of Linear Differential Equations, Oxford Univ. Press1936. Zbl0014.05801JFM62.1277.01
  15. [15] Singer ( M.F.) .- An outline of Differential Galois Theory, Computer Algebra and Differential Equations, E. Tournier Ed., Academic Press1989, pp. 3-57. Zbl0713.12005MR1038057
  16. [16] Whittaker ( E.T.) and Watson ( E.T.) .— A Course of Modern Analysis, Cambridge Univ. Press1927. JFM53.0180.04
  17. [17] Ziglin ( S.L.) .— Branching of solutions and non-existence of first integrals in Hamiltonian mechanics I, Funct. Anal. Appl.16 (1982), pp. 181-189. Zbl0524.58015
  18. [18] Ziglin ( S.L.) .- Branching of solutions and non-existence of first integrals in Hamiltonian mechanics II, Funct. Anal. Appl.17 (1983), pp. 6-17. Zbl0518.58016

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