Article ID Journal Published Year Pages File Type
4666502 Advances in Mathematics 2011 27 Pages PDF
Abstract

This note is concerned with the quantitative recurrence properties of beta dynamical system ([0,1],Tβ)([0,1],Tβ) for general β>1β>1; the size of points with the prescribed recurrence rate is determined. More precisely, Hausdorff dimensions of the sets{x∈[0,1]:|Tβnx−x|<ψ(n) for infinitely many n∈N} and{x∈[0,1]:|Tβnx−x|

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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