Quasianalytic Ilyashenko algebras

Abstract

I construct a quasianalytic field $\mathcal{F}$ of germs at $+\infty$ of real functions with logarithmic generalized power series as asymp\-totic expansions, such that $\mathcal{F}$ is closed under differentiation and $\log$-composition; in particular, $\mathcal{F}$ is a Hardy field. Moreover, the field $\mathcal{F}\circ (-\log )$ of germs at $0^{+}$ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.

27 pages, 1 figure; final changes of section numbering to conform with published version

References in corpus (1)

• The Riemann Mapping Theorem for semianalytic domains and o-minimality