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Artin Approximation Compatible with a Change of Variables

Published online by Cambridge University Press:  20 November 2018

Goulwen Fichou ,
Ronan Quarez  and
Masahiro Shiota
Goulwen Fichou
Affiliation:
IRMAR (UMR 6625), Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France e-mail: goulwen.fichou@univ-rennes1.fr e-mail: ronan.quarez@univ-rennes1.fr
Ronan Quarez
Affiliation:
IRMAR (UMR 6625), Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France e-mail: goulwen.fichou@univ-rennes1.fr e-mail: ronan.quarez@univ-rennes1.fr
Masahiro Shiota
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa, Nagoya, 464-8602, Japan e-mail: shiota@math.nagoya-u.ac.jp
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Abstract

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We propose a version of the classical Artin approximation that allows us to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solution of a Nash equation by a Nash solution in a compatible way with a given Nash change of variables. This result is closely related to the so-called nested Artin approximation and becomes false in the analytic setting. We provide local and global versions of this approximation in real and complex geometry together with an application to the Right-Left equivalence of Nash maps.

Keywords

14P2058A07Artin approximationglobal caseNash functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 4 , 01 December 2016 , pp. 760 - 768
Copyright
Copyright © Canadian Mathematical Society 2016

References

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