Irrational rotation

In the mathematical theory of dynamical systems, an irrational rotation is a map In the mathematical theory of dynamical systems, an irrational rotation is a map where θ is an irrational number. Under the identification of a circle with R/Z, or with the interval with the boundary points glued together, this map becomes a rotation of a circle by a proportion θ of a full revolution (i.e., an angle of 2πθ radians). Since θ is irrational, the rotation has infinite order in the circle group and the map Tθ has no periodic orbits.