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

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dc.creatorCheung, Yitwah
dc.date2004-04-23
dc.date.accessioned2026-07-07T05:07:41Z
dc.date.available2026-07-07T05:07:41Z
dc.descriptionIt 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.
dc.description18 pages published version
dc.identifierhttps://arxiv.org/abs/math/0404433
dc.identifierhttp://arxiv.org/abs/math/0404433
dc.identifierAnn. of Math. (2), Vol. 158 (2003), no. 2, 661--678
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70953
dc.subjectDynamical Systems
dc.subjectNumber Theory
dc.titleHausdorff dimension of the set of nonergodic directions (with an appendix by M. Boshernitzan)
dc.typetext

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