# Morse-Smale Flows on a Tilted Torus

Morse-Smale Flows on a Tilted Torus

This Demonstration shows the gradient flows of the height function on a tilted torus. It illustrates the basic concepts of Morse theory: the critical points of a Morse–Smale function and their stable and unstable manifolds. The position of a point on the tilted torus is determined by two parametrization angles and , which define a local coordinate system at each point of the torus. The parameter (which can be negative) controls the duration of the flow.

-π ≤ α ≤ π

-π ≤ β ≤ π

t