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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**rotation number**which is also sometimes referred to as the map winding**number**... these regions will all result in a motion such that the**rotation number**... region in the bottom-center of the figure correspond to a**rotation number**of ...### Famous quotes containing the words number and/or rotation:

“The world is so full of a *number* of things,

I’m sure we should all be as happy as kings.”

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

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