Quasianalytic Ilyashenko algebras

Abstract We construct a quasianalytic field of germs at +∞ of real functions with logarithmic generalized power series as asymptotic expansions, such that is closed under differentiation and log-composition; in particular, is a Hardy field. Moreover, the field o (−log) of germs at 0 + contains all transition maps of hyperbolic saddles of planar real analytic vector fields.