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Mould Calculus for Hamiltonian Vector Fields

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Date
2008-01
Publisher city
Paris
Publisher
Université Paris Dauphine
Link to item file
http://hal.archives-ouvertes.fr/hal-00207918/en/
Dewey
Analyse
Sujet
normal form; Kolmogorov theorem; Hamiltonian systems; mould calculus; mould; continuous prenormal form
URI
https://basepub.dauphine.fr/handle/123456789/5236
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Morin, Guillaume
Cresson, Jacky
Type
Document de travail / Working paper
Item number of pages
30
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.

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