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20202026
most citedPhysics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification

28 citations · 61 across the 15 of their papers we have counts for

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math.DS2026

A Globally Asymptotically Stable Planar Homogeneous Polynomial Vector Field With No Polynomial Lyapunov Function

Jun Liu, Maxwell Fitzsimmons

We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a…