Universität Augsburg
Institut für Mathematik

I will introduce a normal form for an autonomous Hamiltonian system near an equilibrium point. Special cases of lower order resonances in the two degrees of freedom and their perturbations are treated via a bifurcation theory.

Next, I will present applications. Firstly, I give a new derivation of a Deprits' formula for an isoenergy determinant needed in the KAM theorem in the case of the restricted three-body problem.

I will describe similar results in some cases of the restricted four-body problem.

Next, I will use the Birkhoff normal form in a new proof of a Weinstein' theorem about existence of 1-parameter families of small amplitude periodic solutions near an equilibrium point.

Finally, I will discuss the problem of periodic solutions in the restricted four-body problem.