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# Quasianalytic Ilyashenko algebras

Published:2017-04-27

• Patrick Speissegger,
Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1
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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 asymptotic 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.
 Keywords: generalized series expansion, quasianalyticity, transition map
 MSC Classifications: 41A60 - Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 30E15 - Asymptotic representations in the complex domain 37D99 - None of the above, but in this section 03C99 - None of the above, but in this section

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