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- W3098517802 abstract "For any β > 1, let Tβ : [0, 1) → [0, 1) be the β-transformation defined byTβx = βx mod 1. We study the uniform recurrence properties of the orbit of a point under the β-transformation to the point itself. The size of the set of points with prescribed uniform recurrence rate is obtained. More precisely, for any , the set x∈[0,1):∀N≫1,∃1⩽n⩽N,s.t.|Tβnx−x|⩽β−N is of Hausdorff dimension if and is countable if . In addition, when , it is uncountable but has zero Hausdorff dimension." @default.
- W3098517802 created "2020-11-23" @default.
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- W3098517802 date "2020-07-23" @default.
- W3098517802 modified "2023-09-30" @default.
- W3098517802 title "Uniform recurrence properties for beta-transformation" @default.
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- W3098517802 doi "https://doi.org/10.1088/1361-6544/ab8a65" @default.
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