Artin Approximation Compatible with a Change of Variables
Printed: Dec 2016
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.
Artin approximation, global case, Nash functions
14P20 - Nash functions and manifolds [See also 32C07, 58A07]
58A07 - Real-analytic and Nash manifolds [See also 14P20, 32C07]