Cubic return-map stability of a weak focus
= Cubic return-map stability of a weak focus
{title2=$r\mapsto r+\kappa r^3+O(r^4)$}
If a planar equilibrium with purely imaginary linear <eigenvalues> has radial return map $r\mapsto r+\kappa r^3+O(r^4)$, then $\kappa<0$ gives nonlinear attraction and $\kappa>0$ gives repulsion. Vanishing linear decay therefore does not imply a centre.