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We consider Hamiltonian functions of classical type, namely even and convexwith respect to the generalized momenta. A brake orbit is a periodic solutionof Hamilton's equations such that the generalized momenta are zero on twodifferent points. Under mild assumptions, this paper reduces the multiplicityproblem of the brake orbits for a Hamiltonian function of classical type to themultiplicity problem of orthogonal geodesic chords in a concave Finslerianmanifold with boundary. This paper will be used for a generalization of aSeifert's conjecture about the multiplicity of brake orbits to Hamiltonianfunctions of classical type.

Brake orbits for Hamiltonian systems of classical type via Finsler geodesics