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math.DS2026
Some new criteria for the uniqueness of limit cycles in Rayleigh--Lienard systems
Hebai Chen, Dongmei Xiao, Rui Zhang
In this paper, new uniqueness criteria for Rayleigh--Liénard systems with damping of positive odd degree in the velocity are established. Under suitable conditions, any limit cycle…
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…