Global asymptotic stability of an equilibrium point means that it is stable in the sense of Lyapunov
stability theorem and that every solution exists for all forward time and converges
to the equilibrium. For example, the origin is globally asymptotically stable for
.
Shevchenko, Liu, and Liu (2026) reported that deciding global asymptotic stability of the origin for rational homogeneous polynomial vector fields is undecidable
for every fixed odd degree 
in all sufficiently large fixed dimensions. In particular,
this holds for cubic vector fields, but does not assert undecidability in dimension
3. Their reduction converts degree 
in dimension 
to degree 3 in dimension 
while preserving global asymptotic stability and
Lyapunov stability. Shevchenko, Liu, and Liu (2026) report using GPT-5.6 Sol Ultra
to obtain initial results and assist formalization.
