Orthogonal geodesic chords, brake orbits and homoclinic orbits in Riemannian manifolds (Q2504058)

Homoclinic and certain brake orbits (a special class of oscillating periodic orbits) of Lagrangian rsp. Hamiltonian systems are studied using the associated Jacobi metric. The Maupertius-Jacobi principle is used to show how the multiplicity problem for these types of orbits can be reduced to the study of multiplicity of orthogonal geodesic chords (a geodesic with endpoints on the boundary and tangent orthogonal to the boundary) on a manifold with regular and strongly concave boundary.