Publikation: Quasianalytic Ilyashenko algebras
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2018
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Canadian Journal of Mathematics. 2018, 70(1), pp. 218-240. ISSN 0008-414X. eISSN 1496-4279. Available under: doi: 10.4153/CJM-2016-048-x
Zusammenfassung
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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Fachgebiet (DDC)
510 Mathematik
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generalized series expansion, quasianalyticity, transition map
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SPEISSEGGER, Patrick, 2018. Quasianalytic Ilyashenko algebras. In: Canadian Journal of Mathematics. 2018, 70(1), pp. 218-240. ISSN 0008-414X. eISSN 1496-4279. Available under: doi: 10.4153/CJM-2016-048-xBibTex
@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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<dcterms:abstract xml:lang="eng">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<sup>+</sup> contains all transition maps of hyperbolic saddles of planar real analytic vector fields.</dcterms:abstract>
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