|XXXVIII Workshop on Geometric Methods in Physics||30.06-6.07.2019|
|VIII School on Geometry and Physics||24-28.06.2019|
Birkhoff normalization, Bifurcations of Hamiltonian systems and the Deprits formula
We consider Hamiltonian autonomous systems with n degrees of freedom near a singular point. In the case of absence of resonances of order <5 we present a direct computation of the Birkhoff normal form. In the case of two degrees of freedom we study one-parameter deformations of the 0 : 1; 1 : 1 and 2 : 1 resonant singularities. The obtained results are used in a direct derivation of the Deprits formula for the isoenergetic degeneracy determinant in the restricted three body problem.
Finally, we present a new case of Lyapunov stable libration point in the restricted four body problem.
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