Normalizing Asymptotic Differential Equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908991241584640 |
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| author | Aschenbrenner, Matthias Dries, Lou van den van der Hoeven, Joris |
| author_facet | Aschenbrenner, Matthias Dries, Lou van den van der Hoeven, Joris |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normalizing Asymptotic Differential Equations Aschenbrenner, Matthias Dries, Lou van den van der Hoeven, Joris Commutative Algebra Classical Analysis and ODEs Logic 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]. |
| title | Normalizing Asymptotic Differential Equations |
| topic | Commutative Algebra Classical Analysis and ODEs Logic |
| url | https://arxiv.org/abs/2403.19732 |