= Saddle-focus equilibrium
{title2=$\lambda_u>0,\quad\lambda_s\pm i\omega,\quad\lambda_s<0$}
= Saddle-focus
{synonym}
A three-dimensional <hyperbolic equilibrium point> is a saddle-focus when its <eigenvalues> include a nonreal pair and a real eigenvalue with the opposite sign of real part. In the displayed orientation it has a one-dimensional <unstable manifold> and a two-dimensional spiralling <stable manifold>; reversing time interchanges the stable and unstable dimensions. The ratio $-\lambda_s/\lambda_u$ controls local transverse contraction in a <Shilnikov return map>.
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