The fixed energy problem for a class of nonconvex singular Hamiltonian systems

Carlo Carminati (1) , Eric Séré (2) , Kazunaga Tanaka (3)

1 Università di Pisa, Dipartimento di Matematica
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Department of Mathematics, School of Science and Engineering, Waseda University

We consider a noncompact hypersurface H in R2N which is the energy level of a singular Hamiltonian of “strong force” type. Under global geometric assumptions on H, we prove that it carries a closed characteristic, as a consequence of a result by Hofer and Viterbo 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.

Mots clés: Hamiltonian system; Weinstein conjecture; Strong force; Singular potential; Variational methods; Critical point theory; Cotangent bundle; Closed characteristic; Hypersurface of contact type

Domaines: Mathématiques générales [math.GM]

Carlo Carminati, Eric Séré, Kazunaga Tanaka. The fixed energy problem for a class of nonconvex singular Hamiltonian systems. Journal of Differential Equations, 2006, 230 (1), pp.362-377. ⟨10.1016/j.jde.2006.01.021⟩. ⟨hal-00361397⟩