## Closure under composition?

The Ilyashenko field we construct in our most recent paper is not closed under composition, or even under $\log$-composition. How do we know this? By construction, every LE-series that is the asymptotic expansion of a germ $f$ in the Ilyashenko field $\K$ is an LE-series with convergent LE-monomials, but in general the series is divergent. Since the infinite…