Quasianalytic Ilyashenko algebras

Speissegger, Patrick

Quasianalytic Ilyashenko algebras

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Date

2018

Publication type

Journal article

Publication status

Published

Published in

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.

Subject (DDC)

510 Mathematics

Keywords

generalized series expansion, quasianalyticity, transition map

Cite This

ISO 690

SPEISSEGGER, 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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Refereed

Yes