000002911 001__ 2911
000002911 005__ 20170113100534.0
000002911 037__ $$aSCART-2016-0011
000002911 100__ $$aStolovitch, L
000002911 245__ $$aHolomorphic Normal Form of Nonlinear Perturbations of Nilpotent Vector Fields
000002911 260__ $$c2016
000002911 520__ $$aWe consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension 3. Based on Belitskii’s work, we know that such a vector field is formally conjugate to a (formal) normal form. We give a condition on that normal form which ensures that the normalizing transformation is holomorphic at the fixed point. We shall show that this sufficient condition is a nilpotent version of Bruno’s condition (A). In dimension 2, no condition is required since, according to Strozyna – Zoladek, each such germ is holomorphically conjugate to a Takens normal form. Our proof is based on Newton’s method and sl2(C)-representations.
000002911 594__ $$aNO
000002911 6531_ $$alocal analytic dynamics, fixed point, normal form, Belitskii normal form, small divisors, Newton method, analytic invariant manifold, complete integrability
000002911 700__ $$aVerstringe, F
000002911 773__ $$c410-436$$n4$$pRegular and chaotic dynamics$$v21$$y2016
000002911 85642 $$ahttp://arxiv.org/pdf/1606.07242.pdf
000002911 8560_ $$ffreek.verstringe@observatoire.be
000002911 905__ $$aaccepted to be published in
000002911 980__ $$aREFERD