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Quasianalytic Ilyashenko Algebras

Published online by Cambridge University Press:  20 November 2018

Patrick Speissegger
Patrick Speissegger*
Affiliation:
Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada e-mail: speisseg@math.mcmaster.ca
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Abstract

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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.

Keywords

41A6030E1537D9903C99generalized series expansionquasianalyticitytransition map
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 1 , 01 February 2018 , pp. 218 - 240
Copyright
Copyright © Canadian Mathematical Society 2018

References

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