Morse index properties of colliding solutions to the N-body problem |
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Authors: | Vivina Barutello Simone Secchi |
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Institution: | Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, via Cozzi 53, 20125 Milano, Italy |
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Abstract: | We study a singular Hamiltonian system with an α-homogeneous potential that contains, as a particular case, the classical N-body problem. We introduce a variational Morse-like index for a class of collision solutions and, using the asymptotic estimates near collisions, we prove the non-minimality of some special classes of colliding trajectories under suitable spectral conditions provided α is sufficiently away from zero. We then prove some minimality results for small values of the parameter α. |
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Keywords: | Collision solutions Variational index |
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