Symmetry breaking in Hamiltonian systems
type: Item
instance of: scholarly article
title: Symmetry breaking in Hamiltonian systems
zbMATH Open document ID: 0606.58043
DOI: 10.1016/0022-0396(87)90144-6
author: Vittorio Coti Zelati
author: A. Ambrosetti
author: Ivar Ekeland
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: This paper is devoted to the question whether there exist T-periodic solutions of the Hamiltonian system \[ \dot p=-\frac{\partial H}{\partial q}+\epsilon h_ 1(t)\quad \dot q=\frac{\partial H}{\partial p}+\epsilon h_ 2(t), \] where \(\epsilon >0\) is small, \(h_ 1\) and \(h_ 2\) are T- periodic functions and the unperturbed system \((H_ 0)\) is autonomous. The authors give several theorems concerning the question, provided \((H_ 0)\) fulfills certain additional assumptions (i.e. convexity, growth conditions, integrability conditions etc.). The method they use to prove these theorems depends on an ''abstract'' perturbation result for critical points. This result is proved in the first two sections of the paper.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 3980092
zbMATH Keywords: perturbation of Hamiltonian systems
zbMATH Keywords: perturbation theory for critical points
zbMATH Keywords: T-periodic solutions
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90144-6
OpenAlex ID: W2047652795
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description: scientific article; zbMATH DE number 3980092