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arXiv · 0801.2953

Mould Calculus for Hamiltonian Vector Fields

Jacky Cresson·Guillaume Morin
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Abstract

We present the general framework of Écalle'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 Écalle'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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Jacky Cresson, Guillaume Morin. 2008-01-18. Mould Calculus for Hamiltonian Vector Fields. https://arxiv.org/abs/0801.2953

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