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math.DS2019
A puzzle on the existence of Lyapunov functions for Limit cycle system
Xiao-Liang Gan, Hao-Yu Wang, Ping Ao
Although the limit cycle have been studied for more than 100 years, the existence of its Lyapunov function is still poorly understood. By considering a common limit cycle system, a…
math.DS2019
Does the smooth planar dynamical system with one arbitrary limit cycle always exists smooth Lyapunov function?
Xiao-Liang Gan, Hao-Yu Wang, Ping Ao +1
A rigorous proof of a theorem on the coexistence of smooth Lyapunov function and smooth planar dynamical system with one arbitrary limit cycle is given, combining with a novel deco…