Hausdorff dimension of the set of nonergodic directions (with an appendix by M. Boshernitzan)

Details Hausdorff dimension of the set of nonergodic directions (with an appendix by M. Boshernitzan) Hausdorff dimension of the set of nonergodic directions (with an appendix by M. Boshernitzan)

2004-04-23

arxiv.org/abs/math/0404433v1

Ann. of Math. (2), Vol. 158 (2003), no. 2, 661--678

Mathematics

Dynamical Systems

18 pages published version

Scientific paper

It is known that nonergodic directions in a rational billiard form a subset
of the unit circle with Hausdorff dimension at most 1/2. Explicit examples
realizing the dimension 1/2 are constructed using Diophantine numbers and
continued fractions. A lower estimate on the number of primitive lattice points
in certain subsets of the plane is used in the construction.

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