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arXiv · 2403.19732

Normalizing Asymptotic Differential Equations

Matthias Aschenbrenner·Lou van den Dries·Joris van der Hoeven
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Abstract

We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization theorems for algebraic differential equations over $H$-fields, as a tool in solving such equations in suitable extensions. The results in this monograph are essential in our work on Hardy fields in [6].

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Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven. 2024-03-28. Normalizing Asymptotic Differential Equations. https://arxiv.org/abs/2403.19732

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