# Morse and NonMorse Functions

Here is a contour map of a Morse function. The
island theorem works here. This height function has 6
maxima, 5 minima and 10 saddle points. The total
index is 1.

Here is a contour map of a non-Morse function.
The center is a critical point in which more than two
lines cross. It can not be a classical saddle.
The Morse Lemma prevents this. In this case,
there are 5 maxima, 5 minima and no saddle points.
The central point has index -9. It is a non-Morse
critical point.