= Fold point of a critical manifold
{title2=$F=F_x=0,\quad F_{xx}F_y\ne0$}
= Fold points of a critical manifold
{synonym}
For one fast and one slow variable, a nondegenerate <fold point of a critical manifold> satisfies $F=F_x=0$ and $F_{xx}F_y\ne0$. An attracting and a repelling branch of fast <equilibria> meet there. A slow trajectory reaching the fold generally leaves by a rapid jump when its slow drift crosses the fold transversely. The fold is defined relative to the fast direction: if fast trajectories are slanted in the plotted coordinates, their tangency to the <critical manifold> need not be an extremum of its plotted height.
Back to article page
