Rotation Sets and Complex Dynamics

This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard''s work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of r...