Rotation Number

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.

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Other articles related to "rotation number, number":

Circle Map - Mode Locking
... The limiting behavior in the mode-locked regions is given by the rotation number which is also sometimes referred to as the map winding number ... The values of (K,Ω) in one of 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 ...

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