On the approach of Holmes and Sanders to the Melnikov procedure in the method of averaging
type: Item
instance of: scholarly article
title: On the approach of Holmes and Sanders to the Melnikov procedure in the method of averaging
zbMATH Open document ID: 0552.34039
DOI: 10.1007/BF00949067
author: Daniel Stoffer
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1983-01-01T00:00:00Z
review text: A two-dimensional system (1) \(\dot x=\mu f(t,x,\mu)=\mu f_ 1(x)+\mu^ 2f_ 2(t,x)+..\). is considered where f is periodic in t and \(\mu >0\) is a small parameter. Under the assumption that the equation \(\dot x=\mu f_ 1(x)\) admits two hyperbolic equilibria the author derives a Melnikov type formula for the description of the invariant manifolds of (1).
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 3879334
zbMATH Keywords: small parameter
zbMATH Keywords: Melnikov type formula
zbMATH Keywords: invariant manifolds
reviewed by: S. D. Milusheva
MaRDI profile type: Publication
cites work: Averaging and Chaotic Motions in Forced Oscillations
cites work: Q4769286
cites work: Melnikov's method and averaging
full work available at URL: https://doi.org/10.1007/bf00949067
OpenAlex ID: W1990215273
description: scientific article; zbMATH DE number 3879334