Heaviness in Circle Rotations
نویسنده
چکیده
We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational α modulo one, for all finite portions of the orbit contain at least as many points in the bottom half of the interval as in the top half. Specifically, an inductive procedure for describing the set based on the continued fraction expansion of α is developed, leading into a discussion of the Hausdorff dimension of this set. Depending on the parameter α, all possible dimensions may be achieved, and the essential infimum (with respect to α) of this dimension is positive.
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تاریخ انتشار 2009