The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a curve in the surface of section. If the rotation number is rational, it is called the map winding number, and only a finite number of points in the surface of section will be visited by the trajectory.

# Rotation Number

## See also

Map Winding Number, Quasiperiodic Function, Surface of Section## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Rotation Number."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/RotationNumber.html