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":
... 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 ... 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 ...
Famous quotes containing the words number and/or rotation:
“A considerable percentage of the people we meet on the street are people who are empty inside, that is, they are actually already dead. It is fortunate for us that we do not see and do not know it. If we knew what a number of people are actually dead and what a number of these dead people govern our lives, we should go mad with horror.”
—George Gurdjieff (c. 18771949)
“The lazy manage to keep up with the earths rotation just as well as the industrious.”
—Mason Cooley (b. 1927)