On $k$-summable normal forms of vector fields with one zero eigenvalue
| Autor: | De Maesschalck, Peter, Kristiansen, Kristian Uldall |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we study normal forms of analytic saddle-nodes in $\mathbb C^n$ with any Poincar\'e rank $k\in \mathbb N$. The approach and the results generalize those of Bonchaert and De Maesschalck from 2008 that considered $k=1$. In particular, we introduce a Banach convolutional algebra that is tailored to study differential equations in the Borel plane of order $k$. We anticipate that our approach can stimulate new research and be used to study different normal forms in future work. |
| Databáze: | arXiv |
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