Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8254852 | Chaos, Solitons & Fractals | 2015 | 5 Pages |
Abstract
It was conjectured by Furstenberg that for any xâ[0,1]âQ,dimH{2nx(mod1):nâ¥1}¯+dimH{3nx(mod1):nâ¥1}¯â¥1,where dimH denotes the Hausdorff dimension and A¯ denotes the closure of a set A. When x is a normal number, the above result holds trivially. In this note, we are aiming at giving explicit non-normal numbers for which the above dimensional formula holds.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Wen-Ya Wang,