On existence of infinitely many homoclinic solutions
type: Item
instance of: scholarly article
title: On existence of infinitely many homoclinic solutions
zbMATH Open document ID: 0952.34038
author: Klaudiusz Wójcik
author: Piotr Zgliczyński
published in: Monatshefte für Mathematik
publication date: 2000-08-08T00:00:00Z
review text: Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation \[ \dot z=\bar z(1+\text{e}^{i\varepsilon t}|z|^2),\quad z\in\mathbb{C} . \]
reviewed by: Eugene Ershov
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 1486214
zbMATH Keywords: homoclinic solutions
zbMATH Keywords: isolating segment
zbMATH Keywords: fixed point index
zbMATH Keywords: chaos
MaRDI profile type: Publication
full work available at URL: s006050050006
OpenAlex ID: W1968782335
DOI: 10.1007/S006050050006
description: scientific article; zbMATH DE number 1486214