Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8959547 | Journal of Mathematical Analysis and Applications | 2018 | 13 Pages |
Abstract
In the paper, we investigate a modified version of the shrinking target problem in beta dynamical systems which is induced by the β-transformation Tβ:xâβx(mod1). The Hausdorff dimension of the limâsup setW(f,Ï)={xâ[0,1):|Tβnxâf(x)|<Ï(n)for infinitely many nâN} is determined, where f:[0,1]â[0,1] is a Lipschitz function and Ï is a positive function defined on N. The set W(f,Ï) can be viewed as a dynamical analogue of the inhomogeneous Diophantine approximation in which the inhomogeneous factor is allowed to vary.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Weiliang Wang,