DERIVATIVES OF CIRCLE ROTATIONS AND THE SIMILARITY OF ORBITS

摘要

It is proved that the derivative of a circle rotation on an arbitrary interval is either a circle rotation or a noncyclic exchange of three intervals. In the former case, all possible values of the new angle of rotation are computed. It is shown that the restriction of the orbit of a circle rotation to an eigeninterval of differentiation is similar to the orbit of another circle rotation.