Decidability of Lyapunov stability for quadratic homogeneous vector fields

Determine whether Lyapunov stability of rational quadratic homogeneous vector fields is decidable.

Background

The paper reduces undecidability results for odd-degree homogeneous vector fields to cubic degree, while explaining that its Part I method cannot reach degree two because of an antipodal symmetry obstruction in the angular dynamics. Although the paper discusses degree-two Lyapunov stability as a case mentioned by Arnold, it does not resolve whether the corresponding decision problem is decidable.