On the Reduction of Adiabatic Dynamical Systems near Equilibrium Curves

Nils Berglund
Preprint IPT-EPFL (1998)

Proceedings of the international workshop "Celestial Mechanics, Separatrix Splitting, Diffusion", Aussois, France, June 21-27, 1998.

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.

Keywords and phrases: adiabatic theory, slow--fast systems, invariant manifolds, bifurcation theory, dynamic bifurcations, eigenvalue crossing, resonance


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