Geodesic
Artin Approximation Compatible with a Change of Variables
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 760-768

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DOI

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.
DOI : 10.4153/CMB-2016-034-1
Mots-clés : 14P20, 58A07, Artin approximation, global case, Nash functions 
Fichou, Goulwen; Quarez, Ronan; Shiota, Masahiro. Artin Approximation Compatible with a Change of Variables. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 760-768. doi: 10.4153/CMB-2016-034-1
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     title = {Artin {Approximation} {Compatible} with a {Change} of {Variables}},
     journal = {Canadian mathematical bulletin},
     pages = {760--768},
     year = {2016},
     volume = {59},
     number = {4},
     doi = {10.4153/CMB-2016-034-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-034-1/}
}
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