## Quasianalytic Ilyashenko algebras

The first version of my preprint on quasianalytic Ilyashenko algebras is available on arXiv. Feel free to leave comments here! Here is the abstract: I construct a quasianalytic field $\F$ of germs at $+\infty$ of real functions with logarithmic generalized power series as asymptotic expansions, such that $\F$ is closed under differentiation and log-composition; in…

## Ilyashenko algebras based on log monomials

This post describes the construction of quasianalytic algebras of functions with simple logarithmic transseries as asymptotic expansions. The construction is based on Ilyashenko’s class of almost regular functions, as introduced in his book on Dulac’s problem. This class forms a group under composition, but it is not closed under addition or multiplication; to obtain a…