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- W2009248630 abstract "Let f be a real-analytic function germ at the origin in Rn, whose critical locus contains a given real-analytic set X, and let Y be a germ of a closed subset 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○Φ 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." @default.
- W2009248630 created "2016-06-24" @default.
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- W2009248630 date "2007-04-01" @default.
- W2009248630 modified "2023-09-30" @default.
- W2009248630 title "On the stability of analytic germs under ultradifferentiable perturbations" @default.
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- W2009248630 doi "https://doi.org/10.1016/j.jmaa.2006.06.009" @default.
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