Dimension of the generalized 4-corner set and its projections
Dimension of the generalized 4-corner set and its projections
复制标题
广义四角集的维数及其投影
DOI：
10.1017/s014338571100023x
复制
发表时间：
2011
影响因子：
0.9
通讯作者：
B. Bárány
中科院分区：
文献类型：
--
作者：
B. Bárány
Abstract In the last two decades, considerable attention has been paid to the dimension theory of self-affine sets. In the case of generalized 4-corner sets (see Figure 1), the iterated function systems obtained as the projections of self-affine systems have maps of common fixed points. In this paper, we extend our result [B. Bárány. On the Hausdorff dimension of a family of self-similar sets with complicated overlaps. Fund. Math. 206 (2009), 49–59], which introduced a new method of computation of the box and Hausdorff dimensions of self-similar families where some of the maps have common fixed points. The extended version of our method presented in this paper makes it possible to determine the box dimension of the generalized 4-corner set for Lebesgue-typical contracting parameters.
