A Variational Construction of Chaotic Trajectories for a Reversible Hamiltonian System,

A geometric criterion for the existence of chaotic trajectories of a reversible Hamiltonian system with the configuration spaceT×N, withNa compact manifold, is given. The main result is a variational version of the theorem of D. V. Turayev and L. P. Shilnikov (Dokl. Akad. Nauk SSSR304, 1989, 811–814) on the symbolic representation of trajectories of Hamiltonian systems possessing several homoclinics to a saddle equilibrium