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.
Other articles related to "rotation number, number":
... 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
these several years, each night
as if the room within were aflame.”
—Denise Levertov (b. 1923)
“The lazy manage to keep up with the earths rotation just as well as the industrious.”
—Mason Cooley (b. 1927)