Work

Cyclicity of lips and center-focus problem at infinity

Year: 2026

Type: preprint

Abstract: In this work, we discover an intriguing Liénard 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 Liénard system with center at infinity. In a different direction we improve a lower bound on Hilbert number for Liénard systems. The improvement is due to development of Brudnyi method of calculation of cyclicity of centers near infinity and near zero.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.17773

Authors: Chen, Hebai, Dai, Dehong, Kaloshin, Vadim, Li, Zhijie

Institutions: Central South University, Institute of Science and Technology Austria

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G6478740030, G6717934079

OpenAlex ID: W7203775011

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