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

2006/09/29 by Vivina Barutello, Barutello, Vivina, Simone Secchi +1
Engineering · Physics and Astronomy · #37B30 #37K05 #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.math/0609837

openalex publication_date 2006/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a singular Hamiltonian system with an \al-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 \al is sufficiently away from zero. We then prove some minimality results for small values of the parameter \al.

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