Mould Calculus for Hamiltonian Vector Fields

Details Mould Calculus for Hamiltonian Vector Fields Mould Calculus for Hamiltonian Vector Fields

2008-01-18

arxiv.org/abs/0801.2953v1

Mathematics

Dynamical Systems

30 pages

Scientific paper

We present the general framework of \'Ecalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and calculability. We modify then \'Ecalle's technique to fit in the seek of a formal normal form of a Hamiltonian vector field in cartesian coordinates. We prove that mould calculus can also produce successive canonical transformations to bring a Hamiltonian vector field into a normal form. We then prove a Kolmogorov theorem on Hamiltonian vector fields near a diophantine torus in action-angle coordinates using moulds techniques.

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