Monkey saddle
= Monkey saddle
{title2=$x^3-3xy^2$}
{wiki}
This cubic <smooth function> has one isolated degenerate <critical point> at the origin, with three ascending and three descending sectors. Adding $-tx$ with $t>0$ replaces it by two nondegenerate saddle points at $(\pm\sqrt{t/3},0)$. The <Hessians> there have opposite diagonal entries $6x$ and $-6x$. It illustrates why the number of smooth <critical points> can be smaller than that required for a <Morse function>.