Mould Calculus for Hamiltonian Vector Fields

Morin, Guillaume; Cresson, Jacky

Morin, Guillaume; Cresson, Jacky (2008-01), Mould Calculus for Hamiltonian Vector Fields. https://basepub.dauphine.fr/handle/123456789/5236

Type

Document de travail / Working paper

External document link

http://hal.archives-ouvertes.fr/hal-00207918/en/

Date

2008-01

Publisher

Université Paris Dauphine

Published in

Paris

Metadata

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Author(s)

Morin, Guillaume
Cresson, Jacky

Abstract (EN)

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.

Subjects / Keywords

normal form; Kolmogorov theorem; Hamiltonian systems; mould calculus; mould; continuous prenormal form