Normalizing Asymptotic Differential Equations
Commutative Algebra
2026-04-28 v5 Classical Analysis and ODEs
Logic
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 -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].
Keywords
Cite
@article{arxiv.2403.19732,
title = {Normalizing Asymptotic Differential Equations},
author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
journal= {arXiv preprint arXiv:2403.19732},
year = {2026}
}
Comments
176 pp.; revised based on comments by reviewers; to appear in Memoirs of the European Mathematical Society. arXiv admin note: substantial text overlap with arXiv:2304.10846