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:

“The growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been, is half owing to the *number* who lived faithfully a hidden life, and rest in unvisited tombs.”

—George Eliot [Mary Ann (or Marian)

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

—Mason Cooley (b. 1927)