Box-dimension of the generalized 4-corner set

2010. május 20. csütörtök 16:45

In the last two decades considerable attention has been paid to the dimension theory of self-affine sets. In the case of the generalized four corner sets the IFS obtained as the projection of the self-affine system have maps of common fixed points. We extend our result [1] which introduced a new method of computation of the box and Hausdorff dimension of self-similar families where some of the maps have common fixed point. The extended version of our method makes it possible to determine the box dimension of the generalized four corner set for Lebesgue-typical parameters.

[1] B. Bárány, On The Hausdorff Dimension of a Family of Self-Similar Sets with Complicated Overlaps, Fundamenta Mathematicae, 206, (2009), 49-59.