A Maximum Modulus Theorem for functions admitting Stokes phenomena, and specific cases of Dulac's Theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912067145957376 |
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| author | Palma-Márquez, Jesús Yeung, Melvin |
| author_facet | Palma-Márquez, Jesús Yeung, Melvin |
| contents | We study large classes of real-valued analytic functions that naturally emerge in the understanding of Dulac's problem, which addresses the finiteness of limit cycles in planar differential equations. Building on a Maximum Modulus-type result we got, our main statement essentially follows. Namely, for any function belonging to these classes, the following dichotomy holds: either it has isolated zeros or it coincides with the identity. As an application, we prove that the non-accumulation of limit cycles holds around a specific class of the so-called superreal polycycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Maximum Modulus Theorem for functions admitting Stokes phenomena, and specific cases of Dulac's Theorem Palma-Márquez, Jesús Yeung, Melvin Dynamical Systems 30C80, 34C05, 34C07, 40A30 We study large classes of real-valued analytic functions that naturally emerge in the understanding of Dulac's problem, which addresses the finiteness of limit cycles in planar differential equations. Building on a Maximum Modulus-type result we got, our main statement essentially follows. Namely, for any function belonging to these classes, the following dichotomy holds: either it has isolated zeros or it coincides with the identity. As an application, we prove that the non-accumulation of limit cycles holds around a specific class of the so-called superreal polycycles. |
| title | A Maximum Modulus Theorem for functions admitting Stokes phenomena, and specific cases of Dulac's Theorem |
| topic | Dynamical Systems 30C80, 34C05, 34C07, 40A30 |
| url | https://arxiv.org/abs/2410.07532 |