Quasianalytic Ilyashenko Algebras

Speissegger, Patrick

Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 218-240

Résumé

We 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 $\mathcal{F}\,\circ \,\left( -\text{log} \right)$ of germs at ${{0}^{+}}$ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.

Détail

DOI : 10.4153/CJM-2016-048-x

Mots-clés : 41A60, 30E15, 37D99, 03C99, generalized series expansion, quasianalyticity, transition map

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