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Lyapunov stability of polynomial vector fields is undecidable
We show that there are integers $N$ and odd $D$ such that no algorithm can decide, from the rational coefficients of a homogeneous polynomial vector field F of degree $D$ in dimension $N$, whether the origin is Lyapunov stable for $\dot Y=F(Y)$. This proves, for some large and unoptimized dimension
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