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.

Barutello, V., & Secchi, S. (2008). Morse index properties of colliding solutions to the $N$-body problem. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 25(8), 539-565 [10.1016/j.anihpc.2007.02.005].

Morse index properties of colliding solutions to the $N$-body problem

SECCHI, SIMONE
2008

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.
No
Articolo in rivista - Articolo scientifico
Scientifica
N-body problem
English
539
565
27
Bronze Open Access• Green Open Access
Barutello, V., & Secchi, S. (2008). Morse index properties of colliding solutions to the $N$-body problem. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 25(8), 539-565 [10.1016/j.anihpc.2007.02.005].
Barutello, V; Secchi, S
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/6772
Citazioni
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 13
Social impact