Dynamics of rational surface automorphisms: rotation domains

A Fatou component is said to be a rotation domain if the automorphism induces a torus action on it. We construct a rational surface automorphism with positive entropy and a rotation domain which contains both a curve of fixed points and isolated fixed points. This Fatou component cannot be imbedded into complex Euclidean space, so we introduce a global linear model space and show that it can be globally linearized in this model.