On the monograph "Finiteness Theorems for limit cycles" and a special case of alternant cycles
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909111930585088 |
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| author | Yeung, Melvin |
| author_facet | Yeung, Melvin |
| contents | We provide evidence that the approach of [Ilyashenko 1991] to the proof of Dulac's theorem has a gap. Although the asymptotics of [Ilyashenko 1991] capture far more than the asymptotics of Dulac, we prove that the arguments for why the asymptotics in [Ilyashenko 1991] are not themselves oscillatory is insufficient. We give an explicit counterexample and we draw confines to which Ilyashenko's result may be restricted in order to keep the validity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_12506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the monograph "Finiteness Theorems for limit cycles" and a special case of alternant cycles Yeung, Melvin Dynamical Systems 34C07 (Primary) 34E05 (Secondary) We provide evidence that the approach of [Ilyashenko 1991] to the proof of Dulac's theorem has a gap. Although the asymptotics of [Ilyashenko 1991] capture far more than the asymptotics of Dulac, we prove that the arguments for why the asymptotics in [Ilyashenko 1991] are not themselves oscillatory is insufficient. We give an explicit counterexample and we draw confines to which Ilyashenko's result may be restricted in order to keep the validity. |
| title | On the monograph "Finiteness Theorems for limit cycles" and a special case of alternant cycles |
| topic | Dynamical Systems 34C07 (Primary) 34E05 (Secondary) |
| url | https://arxiv.org/abs/2402.12506 |