English

On the Lagrange-Dirichlet converse in dimension three

Dynamical Systems 2022-08-03 v1

Abstract

Consider a mechanical system with a real analytic potential. We prove that in dimension three, there is an open and dense subset of the set of non strict local minimums of the potential such that every one of its points is a Lyapunov unstable equilibrium point.

Keywords

Cite

@article{arxiv.2208.01139,
  title  = {On the Lagrange-Dirichlet converse in dimension three},
  author = {Juan M. Burgos and Miguel Paternain},
  journal= {arXiv preprint arXiv:2208.01139},
  year   = {2022}
}

Comments

44 pages

R2 v1 2026-06-25T01:23:49.930Z