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

C. Carminati, É Séré, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    We consider a noncompact hypersurface H in R2 N 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.

    Original languageEnglish
    Pages (from-to)362-377
    Number of pages16
    JournalJournal of Differential Equations
    Volume230
    Issue number1
    DOIs
    Publication statusPublished - 2006 Nov 1

    Fingerprint

    Hamiltonians
    Singular Systems
    Electron energy levels
    Hamiltonian Systems
    Lagrangian Systems
    Cotangent Bundle
    Energy
    Energy Levels
    Compact Manifold
    Hypersurface
    Closed
    Theorem
    Class

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

    Cite this

    The fixed energy problem for a class of nonconvex singular Hamiltonian systems. / Carminati, C.; Séré, É; Tanaka, Kazunaga.

    In: Journal of Differential Equations, Vol. 230, No. 1, 01.11.2006, p. 362-377.

    Research output: Contribution to journalArticle

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