Quasianalytic Ilyashenko Algebras

Abstract

A recent result was the construction of a quasianalytic class containing all transition maps at hyperbolic singularities with logarithmic monomials in their series expansions. The end goal being obtaining o-minimality of this structure, we need an extension to several variables stable under certain operations (such as blow-up substitutions). As a first step towards the several variable extension, we construct a quasianalytic Hardy field extending the previous class where the monomials are now allowed to be any definable function in R_an,exp.