The work provides necessary and sufficient conditions for self-affine intersections of homogeneous self-similar sets with translates in R^n, improves dimension results for self-similar cases, and defines multiplicative invariance in Z^n connected to n-torus invariants.
Matilla, Geometry of sets and measures in Euclidean spaces - fractals and rectifiability, Cambridge University Press
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On the intersections of homogeneous self-similar sets with their translates in $\mathbb{R}^{n}$ and a formulation of multiplicative invariance in $\mathbb{Z}^{n}$
The work provides necessary and sufficient conditions for self-affine intersections of homogeneous self-similar sets with translates in R^n, improves dimension results for self-similar cases, and defines multiplicative invariance in Z^n connected to n-torus invariants.