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Integrability of Hamiltonian systems with homogeneous potentials of degree zero |
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| Authors: | Guy Casale Maria Przybylska |
| Institution: | a IRMAR UMR 6625, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France b 1 Chemin du Chateau, 76 430 Les Trois Pierres, France c Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra, Poland d Toruń Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Toruń, Poland |
| Abstract: | We derive necessary conditions for integrability in the Liouville sense of classical Hamiltonian systems with homogeneous potentials of degree zero. We obtain these conditions through an analysis of the differential Galois group of variational equations along a particular solution generated by a non-zero solution d∈Cn of nonlinear equation gradV(d)=d. We prove that when the system is integrable the Hessian matrix V″(d) has only integer eigenvalues and is diagonalizable. |
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