Thumbnail - Request a copy

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

Tanaka, Kazunaga; Séré, Eric; Carminati, Carlo (2006), The fixed energy problem for a class of nonconvex singular Hamiltonian systems, Journal of Differential Equations, 230, 1, p. 362-377. http://dx.doi.org/10.1016/j.jde.2006.01.021

Type
Article accepté pour publication ou publié
Date
2006
Journal name
Journal of Differential Equations
Volume
230
Number
1
Publisher
Elsevier
Pages
362-377
Publication identifier
Metadata
Show full item record
Author(s)
Tanaka, Kazunaga
Séré, Eric
Carminati, Carlo
Abstract (EN)
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.
Subjects / Keywords
Hamiltonian system; Hypersurface of contact type; Closed characteristic; Cotangent bundle; Critical point theory; Variational methods; Singular potential; Strong force; Weinstein conjecture