Functions on the sphere with critical points in pairs and orthogonal geodesic chords

Abstract

Using an estimate on the number of critical points for a Morse-even function on the sphere ${\mathbb{S}}^m$, $m\ge 1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well.

12 pages, 3 figures

References in corpus (2)

• Examples with minimal number of brake orbits and homoclinics in annular potential regions
• Multiple brake orbits in $\mathbf{m}$-dimensional disks