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math.DS2026
Self-similar Delone sets and Pisot numbers
Christoph Bandt, Yves Meyer
We consider Delone point patterns with self-similarity. Under mild conditions, the similarity factor is a Pisot number if and only if the pattern is uniformly discrete. The classic…
math.DS2025
Elementary fractal geometry. 6. The dynamical interior of self-similar sets
Christoph Bandt
On the one hand, the dynamical interior of a self-similar set with open set condition is the complement of the dynamical boundary. On the other hand, the dynamical interior is the…
math.DS2024
Elementary fractal geometry. 5. Weak separation is strong separation
Christoph Bandt, Michael F. Barnsley
For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the fo…