The **rotation number** of *f* is defined in terms of the iterates of *F*:

Henri Poincaré proved that the limit exists and is independent of the choice of the starting point *x*. The lift *F* is unique modulo integers, therefore the rotation number is a well-defined element of **R**/**Z**. Intuitively, it measures the average rotation angle along the orbits of *f*.

Read more about Rotation Number: Properties, See Also

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### Famous quotes containing the words number and/or rotation:

“As Jerome expanded, its chances for the title, “the toughest little town in the West,” increased and when it was incorporated in 1899 the citizens were able to support the claim by pointing to the *number* of thick stone shutters on the fronts of all saloons, gambling halls, and other places of business for protection against gunfire.”

—Administration in the State of Ariz, U.S. public relief program (1935-1943)

“The lazy manage to keep up with the earth’s *rotation* just as well as the industrious.”

—Mason Cooley (b. 1927)