this case, is semiconjugate to the irrational rotation by , and the semiconjugating map of degree 1 is constant on components of the complement of . The rotation number is continuous when viewed as a map from the group of homeomorphisms (with topology) of the circle into the circle. See also Circle map Denjoy diffeomorphism Poincaré section Poincaré recurrence Poincaré–Bendixson theorem References , also SciSpace for smaller file size in pdf ver 1.3 Sebastian van Strien, Rotation Numbers and Poincaré's Theorem (2001) External links Weisstein, Eric W. "Map Winding Number". From MathWorld--A Wolfram Web Resource. Fixed points (mathematics) Dynamical systems