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

### Other articles related to "rotation number, number":

Circle Map - Mode Locking

... in the mode-locked regions is given by the

... in the mode-locked regions is given by the

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

“Among a hundred windows shining

dully in the vast side

of greater-than-palace *number* such-and-such

one burns

these several years, each night

as if the room within were aflame.”

—Denise Levertov (b. 1923)

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

—Mason Cooley (b. 1927)

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