On Hilbert's 16th Problem
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913253319245824 |
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| author | Andersen, Lars |
| author_facet | Andersen, Lars |
| contents | We prove that to each real singularity $f: (\mathbb{R}^{n}, 0) \to (\mathbb{R}^k, 0)$ with $k\geq 2$ one can associate systems of differential equations $\mathfrak{g}^{k}_f$ which are pushforwards in the category of $\mathcal{D}$-modules over $\mathbb{R}^{k}$ of the sheaf of real analytic functions on the total space of the Milnor fibration. We then use this to study Hilbert's 16th problem on polynomial dynamical systems in the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hilbert's 16th Problem Andersen, Lars Algebraic Geometry We prove that to each real singularity $f: (\mathbb{R}^{n}, 0) \to (\mathbb{R}^k, 0)$ with $k\geq 2$ one can associate systems of differential equations $\mathfrak{g}^{k}_f$ which are pushforwards in the category of $\mathcal{D}$-modules over $\mathbb{R}^{k}$ of the sheaf of real analytic functions on the total space of the Milnor fibration. We then use this to study Hilbert's 16th problem on polynomial dynamical systems in the plane. |
| title | On Hilbert's 16th Problem |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.02174 |