[2403.19732] Normalizing Asymptotic Differential Equations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Commutative Algebra arXiv:2403.19732 (math) [Submitted on 28 Mar 2024 ( v1 ), last revised 24 Apr 2026 (this version, v5)] Title: Normalizing Asymptotic Differential Equations Authors: Matthias Aschenbrenner , Lou van den Dries , Joris van der Hoeven View a PDF of the paper titled Normalizing Asymptotic Differential Equations, by Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven View PDF HTML (experimental) 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]. 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 Subjects: Commutative Algebra (math.AC) ; Classical Analysis and ODEs (math.CA); Logic (math.LO) Cite as: arXiv:2403.19732 [math.AC] (or arXiv:2403.19732v5 [math.AC] for this version) https://doi.org/10.48550/arXiv.2403.19732 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Matthias Aschenbrenner [ view email ] [v1] Thu, 28 Mar 2024 13:16:48 UTC (192 KB) [v2] Sat, 1 Nov 2025 09:17:57 UTC (194 KB) [v3] Mon, 2 Mar 2026 15:41:39 UTC (197 KB) [v4] Fri, 13 Mar 2026 08:00:54 UTC (195 KB) [v5] Fri, 24 Apr 2026 10:10:23 UTC (195 KB) Full-text links: Access Paper: View a PDF of the paper titled Normalizing Asymptotic Differential Equations, by Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven View PDF HTML (experimental) TeX Source view license Current browse context: math.AC < prev | next > new | recent | 2024-03 Change to browse by: math math.CA math.LO References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from