Porosity of self-affine sets

Abstract

In this paper, it is proved that any self-affine set satisfying the strong separation condition is uniformly porous. The author constructs a self-affine set which is not porous, although the open set condition holds. Besides, the author also gives a C ¹ iterated function system such that its invariant set is not porous.

Keywords

Porosity / Self-affine set / Open set condition

References

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