 Irrational rotation

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 [0, 1] 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 2"πθ" radians).