Germes de d\'etermination infinie dans des classes lisses |
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Authors: | Vincent Thilliez |
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Institution: | (1) UMR 8524 du CNRS / UFR de Mathéematiques, Université des Sciences et Technologies de Lille, F–59655 Villeneuve d'Ascq Cedex, France., FR |
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Abstract: | We give sufficient conditions of infinite determinacy (in the sense of Mather) with respect to right equivalence, in subrings
of C
∞ (ℝ
n
,0) defined by estimates on successive derivatives, such as rings of Gevrey germs. In this quantitative setting, a defect
(hidden in the classical C
∞ case) appears between the regularity of equivalent germs and the regularity of local diffeomorphisms of (ℝn,0) giving the equivalence. Our conditions yield precise estimates of this defect, related to some suitable Łojasiewicz exponents
of critical loci. We also show that the result is sharp in general.
Received: Received: 27 May 1998 |
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Keywords: | Mathematics Subject Classification (1991): 58C27 26E10 32S99 |
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