98-574 N. Berglund

On the Reduction of Adiabatic Dynamical Systems near Equilibrium Curves (40K, AMS-LaTeX, 2 ps figs) Aug 26, 98

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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.

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