|
|||||
|
|
Dimensions of some fractals defined via the semigroup generated by 2 and 3 |
|
| Authors: | Yuval Peres Joerg Schmeling Stéphane Seuret Boris Solomyak |
| Affiliation: | 1. Microsoft Research, One Microsoft Way, Redmond, WA, 981052, USA 2. Centre for Mathematial Sciences, Lund Institute of Technology/Lund University, Box 118, SE-22100, Line, Sweden 3. Department of Mathematics, LAMA UMR CNRS 8050, Université Paris-Est Créteil, 940010, Créteil Cedex, France 4. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA |
| Abstract: | We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σ m ={0, ...,m?1}? that are invariant under multiplication by integers. The results apply to the sets {x∈Σ m :? k, x k x 2k ... x nk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |