Real Algebraic and Analytic Geometry
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355. Patrick Speissegger:
Quasianalytic Ilyashenko algebras.

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Submission: 2016, June 10.

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

Mathematics Subject Classification (1991): 41A60,30E15,37D99,03C99.

Keywords and Phrases: Generalized series expansions, quasianalyticity, transition maps.

Full text: https://arxiv.org/abs/1606.02751