Quasianalytic Ilyashenko algebras

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2018
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Canadian Journal of Mathematics ; 70 (2018), 1. - pp. 218-240. - ISSN 0008-414X. - eISSN 1496-4279
Abstract
I construct a quasianalytic field F of germs at +∞ 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 o (−log) of germs at 0+ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.
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510 Mathematics
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generalized series expansion, quasianalyticity, transition map
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ISO 690SPEISSEGGER, Patrick, 2018. Quasianalytic Ilyashenko algebras. In: Canadian Journal of Mathematics. 70(1), pp. 218-240. ISSN 0008-414X. eISSN 1496-4279. Available under: doi: 10.4153/CJM-2016-048-x
BibTex
@article{Speissegger2018-02-01Quasi-40969,
  year={2018},
  doi={10.4153/CJM-2016-048-x},
  title={Quasianalytic Ilyashenko algebras},
  number={1},
  volume={70},
  issn={0008-414X},
  journal={Canadian Journal of Mathematics},
  pages={218--240},
  author={Speissegger, Patrick}
}
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