Ray and heteroclinic solutions of Hamiltonian systems with 2 degrees of freedom (Q379612)

The author studies a class of Hamiltonian system with 2 degrees of freedom and a Tonelli Lagrangian. The author shows that at any energy level above a certain critical value of the system, there are ray solutions as in [\textit{V. Bangert}, Calc. Var. Partial Differ. Equ. 2, No. 1, 49--63 (1994; Zbl 0794.58010)] heteroclinic ones between any two periodic neighboring minimal solutions with any prescribed non-trivial homotopy class.The proof is based on an elementary variational method incorporating some arguments of Rabinowitz etc.