Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics

Abstract

Abstract We consider Hamiltonian functions of the classical type, namely, even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton’s equations such that the generalized momenta are zero on two different points. Under mild assumptions, this paper reduces the multiplicity problem of the brake orbits for a Hamiltonian function of the classical type to the multiplicity problem of orthogonal geodesic chords in a concave Finslerian manifold with boundary. This paper will be used for a generalization of a Seifert’s conjecture about the multiplicity of brake orbits to Hamiltonian functions of the classical type.