On the numerical approximation of the rotation number

摘要

The starting point of this paper is a polygonal approximation of an invariant curve of a map. Using this polygonal approximation an approximation for the circle map (the restriction of the map to the invariant curve) is obtained. The rotation number of the circle map is then approximated by the rotation number of the approximated circle map. The error in the obtained approximate rotation number is discussed, and related to the error in the polygonal approximation of the invariant curve. Simple algorithms for the approximation of the rotation number are described. A numerical example illustrates the theory.