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arXiv · 2609.22058

Lyapunov stability of polynomial vector fields is undecidable

Milan Korda
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Abstract

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 and degree, a conjecture of V. I. Arnold.

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Milan Korda. 2026-09-18. Lyapunov stability of polynomial vector fields is undecidable. https://arxiv.org/abs/2609.22058

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