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arXiv · 1806.01732

Ilyashenko algebras based on transserial asymptotic expansions

Zeinab Galal·Tobias Kaiser·Patrick Speissegger
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Abstract

We construct a Hardy field that contains Ilyashenko's class of germs at infinity of almost regular functions as well as all log-exp-analytic germs. In addition, each germ in this Hardy field is uniquely characterized by an asymptotic expansion that is an LE-series as defined by van den Dries et al. As these series generally have support of order type larger than that of the set of natural numbers, the notion of asymptotic expansion itself needs to be generalized.

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BibTeXRIS

Zeinab Galal, Tobias Kaiser, Patrick Speissegger. 2018-06-05. Ilyashenko algebras based on transserial asymptotic expansions. https://arxiv.org/abs/1806.01732

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