On the Stability of Analytic Germs under Ultradifferentiable Perturbations
| dc.creator | Thilliez, Vincent | |
| dc.date | 2006-01-05 | |
| dc.date.accessioned | 2026-07-07T08:07:27Z | |
| dc.date.available | 2026-07-07T08:07:27Z | |
| dc.description | Let $ f$ be a real-analytic function germ whose critical locus contains a given real-analytic set $ X $, and let $ Y $ be a germ of closed subset of $ \mathbb{R}^n $ at the origin. We study the stability of $ f $ under perturbations $ u $ that are flat on $ Y $ and that belong to a given Denjoy-Carleman non-quasianalytic class. We obtain a condition ensuring that $ f+u=f\circΦ$ where $ Φ$ is a germ of diffeomorphism whose components belong to a (generally larger) Denjoy-Carleman class. Roughly speaking, this condition involves a Łojasiewicz-type separation property between $ Y $ and the complex zeros of a certain ideal associated with $ f $ and $ X $. The relationship between the Denjoy-Carleman classes of $ u$ and $ Φ$ is controlled precisely by the inequality. This result extends, and simplifies, former work of the author on germs with isolated critical points. | |
| dc.description | AMS-LaTeX, 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601111 | |
| dc.identifier | http://arxiv.org/abs/math/0601111 | |
| dc.identifier | J. Math. Anal. Appl. 328 (2007), 1141-1151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130944 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 58K40; 26E10; 32B10 | |
| dc.title | On the Stability of Analytic Germs under Ultradifferentiable Perturbations | |
| dc.type | text |