Real Algebraic and Analytic Geometry
Submission: 2016, June 10.
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