Linking and closed orbits
Dynamical Systems
2016-03-17 v2 Mathematical Physics
Differential Geometry
math.MP
Symplectic Geometry
Abstract
We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and the negative set of the potential is non-trivial in the relative homology.
Cite
@article{arxiv.1305.2799,
title = {Linking and closed orbits},
author = {Stefan Suhr and Kai Zehmisch},
journal= {arXiv preprint arXiv:1305.2799},
year = {2016}
}
Comments
We weakened the assumption to be of bounded geometry