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

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Date
2006
Dewey
Probabilités et mathématiques appliquées
Sujet
Hamiltonian system; Hypersurface of contact type; Closed characteristic; Cotangent bundle; Critical point theory; Variational methods; Singular potential; Strong force; Weinstein conjecture
Journal issue
Journal of Differential Equations
Volume
230
Number
1
Publication date
11-2006
Article pages
362-377
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jde.2006.01.021
URI
https://basepub.dauphine.fr/handle/123456789/1025
Collections
  • CEREMADE : Publications
Metadata
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Author
Tanaka, Kazunaga
Séré, Eric
Carminati, Carlo
Type
Article accepté pour publication ou publié
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.

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