Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds
type: Item
instance of: scholarly article
title: Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds
zbMATH Open document ID: 0955.37040
DOI: 10.1016/S0294-1449(99)00102-X
author: Kazunaga Tanaka
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2000-05-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78485
review text: The author deals with the so-called prescribed energy problem: \[ \ddot q+ \nabla V(q)= 0, \qquad \tfrac 12 |\dot q|^2+ V(q)= H, \] where \(q(t): \mathbb{R}\to \mathbb{R}^N \setminus \{0\}\), \(N\geq 2\), \(V: \mathbb{R}^n \setminus \{0\}\to \mathbb{R}\) and \(H\in \mathbb{R}\). The author studies the existence of periodic solutions of similar Hamiltonian systems as well as the existence of closed geodesics on noncompact Riemannian manifolds in a related situation.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1441846
zbMATH Keywords: energy problem
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: closed geodesics
zbMATH Keywords: Riemannian manifold
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
Wikidata QID: Q115339281
OpenAlex ID: W2017540484
description: scientific article; zbMATH DE number 1441846