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math.DS2026
The number of limit cycles of piecewise linear Liénard systems
Hebai Chen, Zhijie Li, Rui Zhang +1
For the planar Liénard differential system , , where is a piecewise linear function, Tonnelier (SIAM J. Appl. Math., 2002) conjectured that the ma…
math.DS2026
Cyclicity of lips and center-focus problem at infinity
Hebai Chen, Dehong Dai, Vadim Kaloshin +1
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 nec…
math.DS2022★ 1 cited
A sufficient and necessary condition of generalized polynomial Liénard systems with global centers
Hebai Chen, Zhijie Li, Rui Zhang
The aim of this paper is to give a sufficient and necessary condition of the generalized polynomial Liénard system with a global center (including linear typer and nilpotent type).…