Infinitely many large amplitude homoclinic orbits for a class of autonomous Hamiltonian systems
type: Item
instance of: scholarly article
title: Infinitely many large amplitude homoclinic orbits for a class of autonomous Hamiltonian systems
zbMATH Open document ID: 0832.34032
published in: Journal of Differential Equations
publication date: 1995-09-25T00:00:00Z
review text: Let \(T\) be a symmetric invertible real matrix which is indefinite, and let \(V\in C^2(\mathbb{R}^2, \mathbb{R})\) satisfy \(V(0)= 0\) and \(\nabla V(0)= 0\). Consider the equation (1) \(Tq''(t)+ \nabla V(q(t))= 0\), \(q\in C^2(\mathbb{R}, \mathbb{R}^2)\), and suppose that \(0\) is a saddle-focus, i.e. the eigenvalues \(\lambda\) of \(\lambda^2 Tq+ V''(0) q= 0\), \(q\in \mathbb{R}^2\), are complex (neither real, nor imaginary). In the present paper, the author proves under some geometrical conditions on \(V_0= \{q: V(q)= 0\}\) that there exist infinitely many homoclinic solutions of (1) and they may be found as limits of periodic solutions.
reviewed by: J.Rogowski
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 800403
zbMATH Keywords: Hamilton systems
zbMATH Keywords: almost periodic
zbMATH Keywords: homoclinic solutions
author: Boris Buffoni
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1123
OpenAlex ID: W2087710774
DOI: 10.1006/JDEQ.1995.1123
description: scientific article; zbMATH DE number 800403