The fixed energy problem for a class of nonconvex singular Hamiltonian systems
We consider a noncompact hypersurface \(\mathcal H\) in \(\mathbb R^{2N}\) which is the energy level of a singular Hamiltonian of `strong force' type. Under global geometric assumptions on \(\mathcal H\), we prove that it carries a closed characteristic, as a consequence of a result by \textit{H. Hofer} and \textit{C. Viterbo} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 15, No.~3, 411--445 (1988; Zbl 0697.58044)] on the Weinstein conjecture in cotangent bundles of compact manifolds. Our theorem contains, as particular cases, earlier results on the fixed energy problem for singular Lagrangian systems of strong force type.
scientific article; zbMATH DE number 5077865
scientific article