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.

Read more about Rotation Number:  Properties, See Also

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