The local Morse Homology of the critical points in the Lagrange problem
Dynamical Systems
2026-03-10 v1 Symplectic Geometry
Abstract
In this paper, we construct local Morse homology in a new way and compute the local Morse homology of the critical points of the Lagrange problem. As a corollary, we prove for the first time that each of the linear critical points is either a saddle point or a degenerate critical point compared to the previous conclusion that if all the linear critical points are non-degenerate, they are saddle points.
Cite
@article{arxiv.2603.07021,
title = {The local Morse Homology of the critical points in the Lagrange problem},
author = {Xiuting Tang},
journal= {arXiv preprint arXiv:2603.07021},
year = {2026}
}