Perturbation geometry for Mathieu's equation
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.
scientific article; zbMATH DE number 3983629