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arXiv:math/0404433 [math.DS]AbstractReferencesReviewsResources

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

Yitwah Cheung

Published 2004-04-23Version 1

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.

Comments: 18 pages published version
Journal: Ann. of Math. (2), Vol. 158 (2003), no. 2, 661--678
Categories: math.DS, math.NT
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