Perturbation geometry for Mathieu's equation
type: Item
instance of: scholarly article
title: Perturbation geometry for Mathieu's equation
zbMATH Open document ID: 0608.34011
author: Z. Afsharnejad
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: For the Mathieu's equation ẍ\(+(\lambda +\mu Cost)x=0\), the partition of the (\(\lambda\),\(\mu)\)-plane into stability and unstability regions provides an understanding of the behaviour of the solutions. The author throws some light on the structure and origin of the transition curves (i.e., the curves separating the stable and unstable regions) by considering these from a geometrical point of view as the inverse images of certain subsets under a smooth map \(\Phi\) from the (\(\lambda\),\(\mu)\)- plane into the four-dimensional space of real \(2\times 2\) matrices.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 3983629
zbMATH Keywords: Mathieu's equation
zbMATH Keywords: transition curves
reviewed by: Prem N. Bajaj
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3983629