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

Henri PoincarĂ© 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:

“A considerable percentage of the people we meet on the street are people who are empty inside, that is, they are actually already dead. It is fortunate for us that we do not see and do not know it. If we knew what a *number* of people are actually dead and what a *number* of these dead people govern our lives, we should go mad with horror.”

—George Gurdjieff (c. 1877–1949)

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

—Mason Cooley (b. 1927)