The fixed energy problem for a class of nonconvex singular Hamiltonian systems
type: Item
instance of: scholarly article
title: The fixed energy problem for a class of nonconvex singular Hamiltonian systems
zbMATH Open document ID: 1104.37039
published in: Journal of Differential Equations
publication date: 2006-12-07T00:00:00Z
review text: We consider a noncompact hypersurface \(\mathcal H\) in \(\mathbb R^{2N}\) which is the energy level of a singular Hamiltonian of `strong force' type. Under global geometric assumptions on \(\mathcal H\), we prove that it carries a closed characteristic, as a consequence of a result by \textit{H. Hofer} and \textit{C. Viterbo} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 15, No.~3, 411--445 (1988; Zbl 0697.58044)] 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.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 5077865
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: Weinstein conjecture
zbMATH Keywords: strong force
zbMATH Keywords: singular potential
zbMATH Keywords: variational methods
zbMATH Keywords: critical point theory
zbMATH Keywords: cotangent bundle
zbMATH Keywords: closed characteristic
zbMATH Keywords: hypersurface of contact type
author: Carlo Carminati
author: Éric Séré
author: Kazunaga Tanaka
MaRDI profile type: Publication
full work available at URL: j.jde.2006.01.021
OpenAlex ID: W2094160272
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DOI: 10.1016/J.JDE.2006.01.021
description: scientific article; zbMATH DE number 5077865