On a galoisian approach to the splitting of separatrices
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 8 (1999) no. 1, p. 125-141
@article{AFST_1999_6_8_1_125_0,
     author = {Morales-Ruiz, Juan J. and Maria Peris, Josep},
     title = {On a galoisian approach to the splitting of separatrices},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 6, 8},
     number = {1},
     year = {1999},
     pages = {125-141},
     zbl = {0971.34076},
     mrnumber = {1721562},
     language = {en},
     url = {http://www.numdam.org/item/AFST_1999_6_8_1_125_0}
}
Morales-Ruiz, Juan J.; Maria Peris, Josep. On a galoisian approach to the splitting of separatrices. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 8 (1999) no. 1, pp. 125-141. http://www.numdam.org/item/AFST_1999_6_8_1_125_0/

[1] Baider (A.), Churchill (R.C.), Rod (D.L.) and Singer (M.F.) .- On the infinitesimal Geometry of Integrate Systems, Preprint 1992. | MR 1365771

[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. | MR 1129412 | Zbl 0739.58018

[3] Churchill (R.C.), Rod (D.L.) and Sleeman (B.D.) .- Symmetric Connections and the Geometry of Doubly-Periodic Floquet Theory, Preprint 1996.

[4] Grotta-Ragazzo (C.) . - Nonintegrability of some Hamiltonian Systems, Scattering and Analytic Continuation, Commun. Math. Phys. 166 (1994), pp. 255-277. | MR 1309550 | Zbl 0814.70009

[5] Kaplansky (I.) .- An Introduction to Differential Algebra, Hermann 1976. | MR 460303

[6] Katz (N.M.) . - A conjecture in the arithmetic theory of differential equations, Bull. Soc. Math. France 110 (1982), pp. 203-239. | Numdam | MR 667751 | Zbl 0504.12022

[7] Kirwan (F.) .- Complex Algebraic Curves, Cambridge Univ. Press 1992. | MR 1159092 | Zbl 0744.14018

[8] Kovacic (J.J.) . - An Algorithm for Solving Second Order Linear Homogeneous Differential Equations, J. Symb. Comput. 2, (1986), pp. 3-43. | MR 839134 | Zbl 0603.68035

[9] Lerman (L.M.) .- Hamiltonian systems with loops of a separatrix of a saddlecenter, Sel. Math. Sov. 10 (1991), pp. 297-306. | MR 1120110 | Zbl 0743.58017

[10] Martinet (J.) and Ramis (J.-P.) .- Théorie de Galois différentielle et resommation, Computer Algebra and Differential Equations, E. Tournier Ed., Academic Press 1989, pp. 117-214. | MR 1038060 | Zbl 0722.12007

[11] Morales-Ruiz (J.J.) and Ramis (J.-P.) .- Galoisian obstructions to integrability of Hamiltonian systems, In preparation.

[12] Morales-Ruiz (J.J.) and Simó (C.) .- Picard-Vessiot Theory and Ziglin's Theorem, J. Diff. Eq. 107 (1994), pp. 140-162. | MR 1260852 | Zbl 0799.58035

[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. | MR 1400798 | Zbl 0866.58034

[14] Poole (E.G.C.) .- Introduction to the theory of Linear Differential Equations, Oxford Univ. Press 1936. | JFM 62.1277.01 | Zbl 0014.05801

[15] Singer (M.F.) .- An outline of Differential Galois Theory, Computer Algebra and Differential Equations, E. Tournier Ed., Academic Press 1989, pp. 3-57. | MR 1038057 | Zbl 0713.12005

[16] Whittaker (E.T.) and Watson ( E.T.) .- A Course of Modern Analysis, Cambridge Univ. Press 1927. | JFM 53.0180.04

[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. | Zbl 0524.58015

[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. | Zbl 0518.58016