Publication date
November 2011
DOI Publisher
Elsevier Inc. ISSN
0001-8708 Citation count (estimate)
26Abstract
AbstractThis 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{x∈[0,1]:|Tβnx−x|<ψ(n) for infinitely many n∈N} and{x∈[0,1]:|Tβnx−x|<e−∑j=0n−1f(Tβjx) for infinitely many n∈N} 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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