Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem
Dynamical Systems
2019-08-02 v3 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
In this paper, we use the central configuration coordinate decomposition to study the linearized Hamiltonian system near the elliptic Euler solutions. Then using the Maslov-type \omega-index theory of symplectic paths and the theory of linear operators we compute the \omega-indices and obtain certain properties of linear stability of the Euler elliptic solutions of the classical three-body problem.
Keywords
Cite
@article{arxiv.1510.06822,
title = {Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem},
author = {Qinglong Zhou and Yiming Long},
journal= {arXiv preprint arXiv:1510.06822},
year = {2019}
}
Comments
42 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1206.6162; text overlap with arXiv:1308.4745 by other authors