Ordinary Differential Equations

From MGSA

Let ${d\over dt}{\mathbf x}=A(t){\mathbf x}$ , where $A (t)$ is a $2\times 2$ periodic matrix with period $ω$ . Are the solutions periodic?
Show that a fundamental matrix is the product of a periodic matrix and an exponential matrix.
What are Floquet multipliers?
Consider ${d\over dt}\begin{pmatrix}x\\ y\end{pmatrix} = \begin{pmatrix}f(x,y)\\ g(x,y)\end{pmatrix}$ , where $f (0,0) = g (0,0) = 0$ . Give examples of what can happen near the origin in terms of eigenvalues. Give assumptions on $f$ and $g$ .

This page was originally derived from this TeX file.