The scanning normal form of linear dynamical systems with variable coefficients (Q804791)

Consider the system \(\dot x=A(t)x,\quad x\in {\mathbb{R}}^ n.\) In the neighbourhood of some \(\tau_ 0\) this system can be written as \(\dot x=(A(\tau_ 0)+\epsilon \gamma (\tau_ 0,\tau))x.\) A change of variables is found in order to give this system the form \(\dot y=B(\tau_ 0,\tau,\epsilon)y,\) where only certain items of B depend on \(\tau\). This last equation can be given the integrable form. Applications to stability and bifurcations are given.