On the Boundary of Self-Affine Sets

Abstract EN

This paper is devoted to studying the boundary behavior of self-affine sets.

We prove that the boundary of an integral self-affine set has Lebesgue measure zero.

In addition, we consider the variety of the boundary of a self-affine set when some other contractive maps are added.

We show that the complexity of the boundary of the new self-affine set may be the same, more complex, or simpler; any one of the three cases is possible.