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 and degree, a conjecture of V. I. Arnold. --- Source: arXiv:2609.22058v1 - http://arxiv.org/abs/2609.22058v1 PDF: https://arxiv.org/pdf/2609.22058v1 Original Link: http://arxiv.org/abs/2609.22058v1...