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arXiv · 1606.02751

Quasianalytic Ilyashenko algebras

Patrick Speissegger
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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.

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Patrick Speissegger. 2016-06-07. Quasianalytic Ilyashenko algebras. https://doi.org/10.4153/cjm-2016-048-x

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