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arXiv · 2608.17773

Cyclicity of lips and center-focus problem near infinity

Hebai Chen·Dehong Dai·Vadim Kaloshin·Zhijie Li
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Abstract

In this work, we discover an intriguing Li\'enard system which is integrable near infinity, integrable near zero and having Ilyashenko-Kotova lips in between. Moreover, we give a necessary and sufficient condition of polynomial Li\'enard system with center at infinity. In a different direction we improve a lower bound on Hilbert number for Li\'enard systems. The improvement is due to development of Brudnyi method of calculation of cyclicity of centers near infinity and near zero.

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Hebai Chen, Dehong Dai, Vadim Kaloshin, Zhijie Li. 2026-08-18. Cyclicity of lips and center-focus problem near infinity. https://arxiv.org/abs/2608.17773

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