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

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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.
18 pages published version

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Dynamical Systems, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/70953

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404433
 http://arxiv.org/abs/math/0404433
 Ann. of Math. (2), Vol. 158 (2003), no. 2, 661--678

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arXiv