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Quasianalytic Ilyashenko algebras

  • 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 generalized series expansion, quasianalyticity, transition map
MSC Classifications: 41A60, 30E15, 37D99, 03C99 show english descriptions Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
Asymptotic representations in the complex domain
None of the above, but in this section
None of the above, but in this section
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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