In 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. Moreover, the orbit of any point x under the iterates of Tθ,
is dense in the interval [0, 1) or the circle.
Read more about Irrational Rotation: Significance
Famous quotes containing the words irrational and/or rotation:
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—Northrop Frye (b. 1912)
“The lazy manage to keep up with the earth’s rotation just as well as the industrious.”
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