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

C. Carminati; É Séré; K. Tanaka

doi:10.1016/j.jde.2006.01.021

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

C. Carminati, É Séré, K. Tanaka^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We consider a noncompact hypersurface H in R^{2 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 language	English
Pages (from-to)	362-377
Number of pages	16
Journal	Journal of Differential Equations
Volume	230
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2006.01.021
Publication status	Published - 2006 Nov 1

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
Applied Mathematics

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10.1016/j.jde.2006.01.021

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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.",

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

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AU - Séré, É

AU - Tanaka, K.

PY - 2006/11/1

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N2 - 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.

AB - 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.

KW - Closed characteristic

KW - Cotangent bundle

KW - Critical point theory

KW - Hamiltonian system

KW - Hypersurface of contact type

KW - Singular potential

KW - Strong force

KW - Variational methods

KW - Weinstein conjecture

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M3 - Article

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SN - 0022-0396

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SP - 362

EP - 377

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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