Finiteness of integrable n-dimensional homogeneous polynomial potentials |
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| Authors: | Maria Przybylska |
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| Institution: | Institut Fourier, UMR 5582 du CNRS, Université de Grenoble I, 100 Rue des Maths, BP 74, 38402 Saint-Martin d''Hères Cedex, France Toruń Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Toruń, Poland |
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| Abstract: | We consider natural Hamiltonian systems of n>1 degrees of freedom with polynomial homogeneous potentials of degree k. We show that under a genericity assumption, for a fixed k, at most only a finite number of such systems is integrable. We also explain how to find explicit forms of these integrable potentials for small k. |
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| Keywords: | 02 30 Hq 02 30 Ik 45 20 Jj |
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