乘法整数作用下分形的不变集的Hausdorff维数
动力系统
2018-02-08 v2
摘要
我们考虑（符号）序列空间中在乘法整数半群作用下不变的子集。一个代表性例子是所有满足对所有有的0-1序列的集合。我们计算了这些集合的Hausdorff维数和Minkowski维数，并表明它们通常是不同的。证明通过乘法子移位的变分原理进行。
引用
@article{arxiv.1102.5136,
title = {Hausdorff dimension for fractals invariant under the multiplicative integers},
author = {Richard Kenyon and Yuval Peres and Boris Solomyak},
journal= {arXiv preprint arXiv:1102.5136},
year = {2018}
}
备注
22 pages, 2 figures; revision after the referee report: corrected minor typos, Example 3.4 expanded, added concluding remarks and references in section 6; accepted for publication in Ergodic Theory and Dynamical Systems