Middle Cantor Set Research Articles

A family of smooth Cantor sets

We show that the Cantor set Cp associated to the sequence {1/n p }n, p > 1, is a smooth attractor. Moreover, it is smoothly conjugate to the 2 p -middle Cantor set. We also study the convolution of Hausdorff measures supported on these sets and the structure and size of the sumset Cp + Cq.

HOMEOMORPHISM CLASSES OF SELF-CONTACTING SYMMETRIC BINARY FRACTAL TREES

We fully describe the homeomorphism classes of self-contacting symmetric binary fractal trees, and provide the explicit homeomorphisms for the classes. In developing this theory, we introduce new notations, definitions and results regarding symmetric binary fractal trees. The set of tip points at maximal height for a class of trees forms a middle Cantor set. We study various aspects of the holes in self-contacting trees, and the hole locator pairs can be used to describe the homeomorphism classes.