Sur la non-int??grabilit?? du probl??me plan des trois corps de masses ??gales, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.331, issue.5, pp.391-394, 2000. ,
DOI : 10.1016/S0764-4442(00)01666-9
Meromorphically integrable homogeneous potentials with multiple Darboux points ,
Third order integrability conditions for homogeneous potentials of degree ???1, Journal of Mathematical Physics, vol.53, issue.8, 2012. ,
DOI : 10.1063/1.4746691
Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra, pp.7-10, 1992. ,
Computing in algebraic geometry, 2006. ,
Obstruction de Jordan ?? l???int??grabilit?? de syst??mes hamiltoniens avec potentiel homog??ne, Annales de l???institut Fourier, vol.59, issue.7, pp.2839-2890, 2009. ,
DOI : 10.5802/aif.2510
A search for integrable two-dimensional hamiltonian systems with polynomial potential, Physics Letters A, vol.96, issue.6, pp.273-278, 1983. ,
DOI : 10.1016/0375-9601(83)90178-0
On a Diophantine Problem, The American Mathematical Monthly, vol.28, issue.8/9, pp.300-303, 1921. ,
DOI : 10.2307/2971778
On Riemann's equations which are solvable by quadratures, Funkcial. Ekvac, vol.12, pp.269-281, 1969. ,
Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4, Journal of Mathematical Physics, vol.52, issue.1, p.12702, 2011. ,
DOI : 10.1063/1.3544473
Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree ??? 3, Physica D: Nonlinear Phenomena, vol.240, issue.24, pp.1928-1935, 2011. ,
DOI : 10.1016/j.physd.2011.09.003
All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3, Physics Letters A, vol.327, issue.5-6, pp.5-6461, 2004. ,
DOI : 10.1016/j.physleta.2004.05.042
Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential, Journal of Mathematical Physics, vol.46, issue.6, p.62901, 2005. ,
DOI : 10.1063/1.1917311
Necessary conditions for super-integrability of Hamiltonian systems, Physics Letters A, vol.372, issue.34, pp.5581-5587, 2008. ,
DOI : 10.1016/j.physleta.2008.06.065
Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.38, p.43382001, 2010. ,
DOI : 10.1088/1751-8113/43/38/382001
Necessary conditions for the existence of additional first integrals for Hamiltonian systems with homogeneous potential, Nonlinearity, vol.25, issue.2, pp.255-277, 2012. ,
DOI : 10.1088/0951-7715/25/2/255
Non-integrability of the degenerate cases of the swinging Atwood's machine using higher order variational equations, Discrete Contin. Dyn. Syst, vol.29, issue.1, pp.1-24, 2011. ,
Galoisian obstructions to integrability of Hamiltonian systems, Methods and Applications of Analysis, vol.8, issue.1, pp.33-95, 2001. ,
DOI : 10.4310/MAA.2001.v8.n1.a3
Galoisian obstructions to integrability of Hamiltonian systems, Methods and Applications of Analysis, vol.8, issue.1, pp.97-111, 2001. ,
DOI : 10.4310/MAA.2001.v8.n1.a3
A note on the non-integrability of some Hamiltonian systems with a homogeneous potential, Methods and Applications of Analysis, vol.8, issue.1, pp.113-120, 2001. ,
DOI : 10.4310/MAA.2001.v8.n1.a5
Integrability of Hamiltonian systems and differential Galois groups of higher variational equations, Ann. Sci. École Norm. Sup, issue.46, pp.40845-884, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00635878
On the meromorphic non-integrability of some $N$-body problems, Discrete and Continuous Dynamical Systems, vol.24, issue.4, pp.1225-1273, 2009. ,
DOI : 10.3934/dcds.2009.24.1225
A list of all integrable two-dimensional homogeneous polynomial potentials with a polynomial integral of order at most four in the momenta, Journal of Physics A: Mathematical and General, vol.34, issue.41, pp.348611-8630, 2001. ,
DOI : 10.1088/0305-4470/34/41/316
Finiteness of integrable n-dimensional homogeneous polynomial potentials, Physics Letters A, vol.369, issue.3, pp.180-187, 2007. ,
DOI : 10.1016/j.physleta.2007.04.077
Non-integrability of some Hamiltonian systems in polar coordinates, Journal of Physics A: Mathematical and General, vol.30, issue.16, pp.305869-5876, 1997. ,
DOI : 10.1088/0305-4470/30/16/026
Non-integrability of the collinear three-body problem, Discrete and Continuous Dynamical Systems, vol.30, issue.1, pp.299-312, 2011. ,
DOI : 10.3934/dcds.2011.30.299
Darboux points and integrability analysis of Hamiltonian systems with homogeneous rational potentials, Physica D: Nonlinear Phenomena, vol.249, pp.1-15, 2013. ,
DOI : 10.1016/j.physd.2012.12.012
The meromorphic non-integrability of the three-body problem, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2001, issue.537, pp.127-149, 2001. ,
DOI : 10.1515/crll.2001.061
Integrability of Hamiltonians with polynomial potentials, Selected papers from the Conference on Computational and Mathematical Methods for Science and Engineering, pp.213-224, 2002. ,
DOI : 10.1016/S0377-0427(03)00467-9
Comprehensive Gr??bner bases, Journal of Symbolic Computation, vol.14, issue.1, pp.1-29, 1992. ,
DOI : 10.1016/0747-7171(92)90023-W
A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential, Physica D: Nonlinear Phenomena, vol.29, issue.1-2, pp.128-142, 1987. ,
DOI : 10.1016/0167-2789(87)90050-9