Quantitative recurrence properties for beta-dynamical system |
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| Authors: | Bo Tan Bao-Wei Wang |
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| Affiliation: | aSchool of Mathematics and Statistics, Huazhong University of Science and Technology, 430074 Wuhan, PR China;bLAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France |
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| Abstract: | This note is concerned with the quantitative recurrence properties of beta dynamical system ([0,1],Tβ) for general β>1; the size of points with the prescribed recurrence rate is determined. More precisely, Hausdorff dimensions of the sets and are obtained completely, where ψ is a positive function defined on N and f is a positive continuous function on [0,1]. Besides, the pressure function P(f,Tβ) with a continuous potential f is proven to be continuous with respect to β. |
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| Keywords: | MSC: 11K55 28A80 |
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