An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the Newtonian $n$-body Problem

no code implementations • 5 Oct 2019 • Xijun Hu, Yuwei Ou, Guowei Yu

Moreover for homothetic solutions with arbitrary energy, we give a simple and precise formula that relates the Morse indices of these homothetic solutions to the spectra of the normalized potential at the corresponding central configurations.

Dynamical Systems 70F16, 70F10, 37J45, 53D12