XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Henryk Żołądek## Birkhoff normalization, Bifurcations of Hamiltonian systems and the Deprits formulaWe 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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University of Bialystok |

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