On the Frequency of Balanced Times in Cylinder Flows

Details On the Frequency of Balanced Times in Cylinder Flows On the Frequency of Balanced Times in Cylinder Flows

2009-08-31

arxiv.org/abs/0908.4547v1

Mathematics

Dynamical Systems

15 Pages

Scientific paper

Given an irrational alpha and an x in the unit interval, the set of balanced times, for which the same number of (k*alpha+x) (modulo one) are less than or equal to one half as are larger than one half, is in general infinite, but sparse in terms of density. We investigate the sparseness of this sequence in terms of summation over reciprocals. Our results are that for the generic pair (alpha,x), the resulting sum diverges, but there are certain exceptional alpha for which the associated sums converge for every x.

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