Splitting differential equations using Galois theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917960369569792 |
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| author | Eagles, Christine Jimenez, Léo |
| author_facet | Eagles, Christine Jimenez, Léo |
| contents | This article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is internal to the constants, we would like to determine when its pullback is itself internal to the constants. To do so, we develop, using model-theoretic Galois theory and differential algebra, a connection between internality of the pullback and the splitting of a short exact sequence of algebraic Galois groups. We then use algebraic group theory to obtain internality and non-internality results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting differential equations using Galois theory Eagles, Christine Jimenez, Léo Logic 03C45, 03C98, 12H05, 12L12 This article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is internal to the constants, we would like to determine when its pullback is itself internal to the constants. To do so, we develop, using model-theoretic Galois theory and differential algebra, a connection between internality of the pullback and the splitting of a short exact sequence of algebraic Galois groups. We then use algebraic group theory to obtain internality and non-internality results. |
| title | Splitting differential equations using Galois theory |
| topic | Logic 03C45, 03C98, 12H05, 12L12 |
| url | https://arxiv.org/abs/2403.14900 |