Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles
Dynamical Systems
2018-07-04 v1
Abstract
We use nonsmooth critical point theory and the theory of geodesics with obstacle to show a multiplicity result about orthogonal geodesic chords in a Riemannian manifold (with boundary) which is homeomorphic to an -disk. This applies to brake orbits in a potential well of a natural Hamiltonian system, providing a further step towards the proof of a celebrated conjecture by Seifert.
Keywords
Cite
@article{arxiv.1807.00887,
title = {Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles},
author = {Roberto Giambò and Fabio Giannoni and Paolo Piccione},
journal= {arXiv preprint arXiv:1807.00887},
year = {2018}
}
Comments
24 pages. Accepted for publication on Calc Var PDE