Quasianalytic Ilyashenko Algebras

@article{Speissegger2018QuasianalyticIA,
  title={Quasianalytic Ilyashenko Algebras},
  author={P. Speissegger},
  journal={Canadian Journal of Mathematics},
  year={2018},
  volume={70},
  pages={218 - 240}
}
  • P. Speissegger
  • Published 2018
  • Mathematics
  • Canadian Journal of Mathematics
Abstract 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. 
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