Multiple orthogonal geodesic chords and a proof of Seifert's conjecture on brake orbits

Abstract

Using nonsmooth critical point theory, we prove the existence of at least N orthogonal geodesic chords in a class of Riemannian N-disk with strongly concave boundary. This yields a proof of a celebrated conjecture by H.Seifert on the number of brake orbits in a potential well of a natural Lagrangian/Hamiltonian system.

35 pages

References in corpus (1)

• Examples with minimal number of brake orbits and homoclinics in annular potential regions

Cited by in corpus (1)

• Brake orbits for Hamiltonian systems of classical type via Finsler geodesics