Keplerian orbits through the Conley-Zehnder index
Dynamical Systems
2023-01-10 v2 Mathematical Physics
math.MP
Abstract
It was discovered by Gordon in 1977 that Keplerian ellipses in the plane are minimizers of the Lagrangian action and spectrally stable as periodic points of the associated Hamiltonian flow. The aim of this paper is to give a homotopy theoretical proof of these results through a self-contained, explicit and simple computation of the Conley-Zehnder index. The techniques developed in this paper can be used to investigate the higher dimensional case of Keplerian ellipses, where the classical variational proof no longer applies.
Cite
@article{arxiv.1908.00075,
title = {Keplerian orbits through the Conley-Zehnder index},
author = {Henry Kavle and Daniel Offin and Alessandro Portaluri},
journal= {arXiv preprint arXiv:1908.00075},
year = {2023}
}
Comments
21 pages, 3 figures