Polynomial reformulation of the Kuo criteria for v-sufficiency of map-germs

Abstract

In the paper a set of necessary and sufficient conditions for \textit{v-}sufficiency (equiv. \textit{sv-}sufficiency) of jets of map-germs $f:({\mathbb{R}}^n,0)\to ({\mathbb{R}}^m,0)$ is proved which generalize both the Kuiper-Kuo and the Thom conditions in the function case ($m=1$) so as the Kuo conditions in the general map case ($m>1$). Contrary to the Kuo conditions the conditions proved in the paper do not require to verify any inequalities in a so-called horn-neighborhood of the (a'priori unknown) set $f^{-1}(0)$. Instead, the proposed conditions reduce the problem on \textit{v-}sufficiency of jets to evaluating the local Łojasiewicz exponents for some constructively built polynomial functions.

arXiv comment16 pages, 25 bibliography references, corrected misprints Accepted for publication in DCDS-B, added acknowledgments to the supporting grant

References in corpus (3)

• A set on which the Lojasieewicz exponent at infinity is attained
• An Effective Łojasiewicz Inequality for Real Polynomials
• On the Lojasiewicz exponent of the gradient of a polynomial function

Cited by in corpus (1)

• Hierarchical stratification of Pareto sets