DERIVATIVES OF CIRCLE ROTATIONS AND THE SIMILARITY OF ORBITS


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Abstract

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. Bibliography: 9 titles.

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