N. Berglund
On the Reduction of Adiabatic Dynamical Systems
near Equilibrium Curves
(40K, AMS-LaTeX, 2 ps figs)
ABSTRACT. We consider adiabatic differential equations of the form
e dx/dt = f(x,t), where e is a small parameter. A few results on the
behaviour of solutions close to an equilibrium curve of f are reviewed,
including existence of tracking solutions, dynamic diagonalization and
linearization, and invariant manifolds. We then point out some interesting
connections between the effect of bifurcations, eigenvalues crossings and
resonances.