A KAM phenomenon for singular holomorphic vector fields
Identifieur interne : 000255 ( France/Analysis ); précédent : 000254; suivant : 000256A KAM phenomenon for singular holomorphic vector fields
Auteurs : Laurent Stolovitch [France]Source :
- Publications Mathématiques de l'Institut des Hautes Études Scientifiques [ 0073-8301 ] ; 2005-12-01.
Abstract
Abstract: Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection of a polydisc with an analytic set of the form “resonant monomials = constants”. Such a biholomorphism conjugates the restriction of X to one of its invariant varieties to the restriction of a linear diagonal vector field to a toric variety. Moreover, we show that the set of “frequencies” defining the invariant sets is of positive measure.
Url:
DOI: 10.1007/s10240-005-0035-0
Affiliations:
- France
- Midi-Pyrénées, Occitanie (région administrative)
- Toulouse
- Université Toulouse III - Paul Sabatier
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ISTEX:8713D070D43E44A0432E4D0A3CC83FCAD90956E0Le document en format XML
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