On $k$-summable normal forms of vector fields with one zero eigenvalue
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911300863393792 |
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| author | De Maesschalck, Peter Kristiansen, Kristian Uldall |
| author_facet | De Maesschalck, Peter Kristiansen, Kristian Uldall |
| contents | In this paper, we study normal forms of analytic saddle-nodes in $\mathbb C^{n+1}$ with any Poincaré rank $k\in \mathbb N$. The approach and the results generalize those of Bonckaert 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 $k$. One of the subtleties that we take care of in this paper, is that nontrivial Jordan blocks are allowed in the linear part of the vector field. We anticipate that our approach can stimulate new research and be used to study different normal forms in future work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $k$-summable normal forms of vector fields with one zero eigenvalue De Maesschalck, Peter Kristiansen, Kristian Uldall Dynamical Systems In this paper, we study normal forms of analytic saddle-nodes in $\mathbb C^{n+1}$ with any Poincaré rank $k\in \mathbb N$. The approach and the results generalize those of Bonckaert 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 $k$. One of the subtleties that we take care of in this paper, is that nontrivial Jordan blocks are allowed in the linear part of the vector field. We anticipate that our approach can stimulate new research and be used to study different normal forms in future work. |
| title | On $k$-summable normal forms of vector fields with one zero eigenvalue |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.20854 |