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2 results

  • Artin Approximation Compatible with a Change of Variables

  • Goulwen Fichou, Ronan Quarez, Masahiro Shiota
  • Journal:
    Canadian Mathematical Bulletin / Volume 59 / Issue 4 / 01 December 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 760-768
    Print publication:
    01 December 2016
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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.

  • Blow Analytic Mappings and Functions

  • Etsuo Yoshinaga
  • Journal:
    Canadian Mathematical Bulletin / Volume 36 / Issue 4 / 01 December 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 497-506
    Print publication:
    01 December 1993
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  • Let π: M —> Rn be the blowing-up of Rn at the origin. Then a continuous map-germ f: (Rn — 0,0) —> Rm is called blow analytic if there exists an analytic map-germ such that Then an inverse mapping theorem for blow analytic mappings as a generalization of classical theorem is shown. And the following is shown. Theorem: The analytic family of blow analytic functions with isolated singularities admits an analytic trivialization after blowing-up.