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May 2008 $C^{\ell}$-$G$-triviality of map germs and Newton polyhedra, $G = \mathcal R$, $\mathcal C$ and $\mathcal K$
Marcelo José SAIA, Carlos Humberto Soares JÚNIOR
Hokkaido Math. J. 37(2): 331-348 (May 2008). DOI: 10.14492/hokmj/1253539558

Abstract

We provide estimates for the $C^{\ell}$-$G$-triviality, for $ 0 \leq \ell < \infty$ and $G$ is one of Mather's groups ${\mathcal R}$, ${\mathcal C}$ or ${\mathcal K}$, of deformations of analytic map germs $f: (\mathbb{R}^n,0) \to (\mathbb{R}^p,0)$ of type $f_t(x)=f(x)+θ(x,t)$ which satisfy a non-degeneracy condition with respect to some Newton polyhedron. We apply the method of construction of controlled vector fields and, for each group $G$, the control function is determined from the choice of a convenient {\it Newton filtration } in the ring of real analytic germs. The results are given in terms of the filtration of the coordinate function germs $f_1, \ldots , f_p$ of $f$.

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Marcelo José SAIA. Carlos Humberto Soares JÚNIOR. "$C^{\ell}$-$G$-triviality of map germs and Newton polyhedra, $G = \mathcal R$, $\mathcal C$ and $\mathcal K$." Hokkaido Math. J. 37 (2) 331 - 348, May 2008. https://doi.org/10.14492/hokmj/1253539558

Information

Published: May 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1207.58032
MathSciNet: MR2415904
Digital Object Identifier: 10.14492/hokmj/1253539558

Subjects:
Primary: 58C27

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 2 • May 2008
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