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arXiv · 2402.12506

On the monograph "Finiteness Theorems for limit cycles" and a special case of alternant cycles

Melvin Yeung
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Abstract

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.

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Melvin Yeung. 2024-02-19. On the monograph "Finiteness Theorems for limit cycles" and a special case of alternant cycles. https://arxiv.org/abs/2402.12506

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