Abstract:The paper concerns the dynamics-related properties of the rotation map of a circle (rotation of the plane). A self-similar structure of orbits of the rotation map is established. That is, a possibility of decomposition of orbits of a given rotation map into a finite set of orbits of other such maps is proved-it is shown that every orbit of iterates of the rotation of circle on irrational angle, after linear re-scaling of its argument can be represented as a finite set of such orbits situated on another circles… Show more
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