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Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations
1. | Laboratoire de Mathématiques et d'Informatique (LMI), INSA de Rouen, Avenue de l'Université, 76 801 Saint Etienne du Rouvray Cedex, France |
2. | Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417, Zielona Góra, Poland |
References:
[1] |
M. Audin, Les Systèmes Hamiltoniens et Leur Intégrabilité,, Cours Spécialisés 8, (2001).
|
[2] |
A. Baider, R. C. Churchill, D. L. Rod and M. F. Singer, On the infinitesimal geometry of integrable systems,, in Mechanics Day (Waterloo, (1992), 5.
|
[3] |
G. Casale, Morales-Ramis theorems via Malgrange pseudogroup,, Annales de l'Institut Fourier, 59 (2009), 2593.
doi: 10.5802/aif.2501. |
[4] |
G. Duval and A. J. Maciejewski, Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials,, Annales de l'Institut Fourier, 59 (2009), 2839.
doi: 10.5802/aif.2510. |
[5] |
N. V. Grigorenko, Abelian extensions in Picard-Vessiot theory,, Mat. Zametki, 17 (1975), 113.
|
[6] |
J. E. Humphreys, Linear Algebraic Groups,, Graduate Texts in Mathematics, (1975).
|
[7] |
E. R. Kolchin, Algebraic groups and algebraic dependence,, Amer. J. Math., 90 (1968), 1151.
doi: 10.2307/2373294. |
[8] |
A. J. Maciejewski and M. Przybylska, Differential Galois theory and integrability,, Internat. J. Geom. Methods in Modern Phys., 6 (2009), 1357.
doi: 10.1142/S0219887809004272. |
[9] |
J. J. Morales-Ruiz and J.-P. Ramis, Integrability of dynamical systems through differential Galois theory: A practical guide,, in Differential algebra, 509 (2010), 143.
doi: 10.1090/conm/509/09980. |
[10] |
J. J. Morales-Ruiz, J. P. Ramis and C. Simó, Integrability of Hamiltonian systems and differential Galois groups of higher variational equations,, Ann. Sci. Éc. Norm. Supér, 40 (2007), 845.
doi: 10.1016/j.ansens.2007.09.002. |
[11] |
M. van der Put and M. F. Singer, Galois Theory of Linear Differential Equations, vol. 328 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences],, Springer-Verlag, (2003).
|
show all references
References:
[1] |
M. Audin, Les Systèmes Hamiltoniens et Leur Intégrabilité,, Cours Spécialisés 8, (2001).
|
[2] |
A. Baider, R. C. Churchill, D. L. Rod and M. F. Singer, On the infinitesimal geometry of integrable systems,, in Mechanics Day (Waterloo, (1992), 5.
|
[3] |
G. Casale, Morales-Ramis theorems via Malgrange pseudogroup,, Annales de l'Institut Fourier, 59 (2009), 2593.
doi: 10.5802/aif.2501. |
[4] |
G. Duval and A. J. Maciejewski, Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials,, Annales de l'Institut Fourier, 59 (2009), 2839.
doi: 10.5802/aif.2510. |
[5] |
N. V. Grigorenko, Abelian extensions in Picard-Vessiot theory,, Mat. Zametki, 17 (1975), 113.
|
[6] |
J. E. Humphreys, Linear Algebraic Groups,, Graduate Texts in Mathematics, (1975).
|
[7] |
E. R. Kolchin, Algebraic groups and algebraic dependence,, Amer. J. Math., 90 (1968), 1151.
doi: 10.2307/2373294. |
[8] |
A. J. Maciejewski and M. Przybylska, Differential Galois theory and integrability,, Internat. J. Geom. Methods in Modern Phys., 6 (2009), 1357.
doi: 10.1142/S0219887809004272. |
[9] |
J. J. Morales-Ruiz and J.-P. Ramis, Integrability of dynamical systems through differential Galois theory: A practical guide,, in Differential algebra, 509 (2010), 143.
doi: 10.1090/conm/509/09980. |
[10] |
J. J. Morales-Ruiz, J. P. Ramis and C. Simó, Integrability of Hamiltonian systems and differential Galois groups of higher variational equations,, Ann. Sci. Éc. Norm. Supér, 40 (2007), 845.
doi: 10.1016/j.ansens.2007.09.002. |
[11] |
M. van der Put and M. F. Singer, Galois Theory of Linear Differential Equations, vol. 328 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences],, Springer-Verlag, (2003).
|
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