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^*

^*この研究の対応する著者

基幹理工学部

研究成果: Article › 査読

11 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	362-377
ページ数	16
ジャーナル	Journal of Differential Equations
巻	230
号	1
DOI	https://doi.org/10.1016/j.jde.2006.01.021
出版ステータス	Published - 2006 11 1

ASJC Scopus subject areas

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応用数学

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10.1016/j.jde.2006.01.021

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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.

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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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DO - 10.1016/j.jde.2006.01.021

M3 - Article

AN - SCOPUS:33748278714

VL - 230

SP - 362

EP - 377

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -

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

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