Symplectic transformations and periodic solutions of Hamiltonian systems
type: Item
instance of: scholarly article
title: Symplectic transformations and periodic solutions of Hamiltonian systems
zbMATH Open document ID: 0941.37041
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-08-13T00:00:00Z
review text: The paper deals with the existence of periodic solutions of Hamiltonian systems, both for the first-order Hamiltonian systems \[ \dot x=Hy(t,x,y),\quad \dot y=-H_x(t,x,y)\tag{1} \] and the second-order Hamiltonian systems \[ -\ddot y=V_y(t,y).\tag{2} \] Note that equation (2) is a special case of (1) with \(H=\frac 12|x|^2+V(t,y)\). The aim of this paper is to understand the relationship between (1) and (2). The author shows that a superquadratic (subquadratic) (2) is equivalent to superquadratic (subquadratic) (1) by a symplectic transformation.
Mathematics Subject Classification ID: 37J10
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 1218641
zbMATH Keywords: periodic solutions
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: symplectic transformation
author: Meiyue Jiang
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6010
OpenAlex ID: W1968634836
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DOI: 10.1006/JMAA.1998.6010
description: scientific article; zbMATH DE number 1218641