1. CMB Online first
||Artin approximation compatible with a change of variables|
We propose a version of the classical Artin
which allows 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:Artin approximation, global case, Nash functions
2. CMB 2011 (vol 55 pp. 752)
||Approximation of Holomorphic Solutions of a System of Real Analytic Equations|
We prove the existence of an approximation function for holomorphic
solutions of a system of real analytic equations. For this we use
ultraproducts and Weierstrass systems introduced by J. Denef and L.
Lipshitz. We also prove a version of the PÅoski smoothing theorem in
Keywords:Artin approximation, real analytic equations
Categories:13B40, 13L05, 14F12