A KAM phenomenon for singular holomorphic vector fields
| dc.creator | Stolovitch, L. | |
| dc.date | 2005-03-31 | |
| dc.date | 2005-04-01 | |
| dc.date.accessioned | 2026-07-07T05:18:42Z | |
| dc.date.available | 2026-07-07T05:18:42Z | |
| dc.description | Let $X$ be a germ of holomorphic vector field at the origin of ${\bf C}^n$ and vanishing there. We assume that $X$ is a "nondegenerate" good perturbation of a 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. 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. | |
| dc.description | 62 pages, 3 figures, to appear in Publ. Math. I.H.E.S | |
| dc.identifier | https://arxiv.org/abs/math/0503749 | |
| dc.identifier | http://arxiv.org/abs/math/0503749 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74753 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | Complex Variables | |
| dc.title | A KAM phenomenon for singular holomorphic vector fields | |
| dc.type | text |