Finite type in measure sense for self-similar sets with overlaps
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DOI: 10.1007/s00209-020-02632-3
Abstract: For self-similar sets with overlaps, we introduce a notion named the finite type in measure sense and reveal its intrinsic relationships with the weak separation condition and the generalized finite type. read more here.
Keywords: finite type; self similar; similar sets; measure sense ... See more keywords
Arithmetic progressions in self-similar sets
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DOI: 10.1007/s11464-019-0788-2
Abstract: Given a sequence $\{b_{i}\}_{i=1}^{n}$ and a ratio $\lambda \in (0,1),$ let $E=\cup_{i=1}^n(\lambda E+b_i)$ be a homogeneous self-similar set. In this paper, we study the existence and maximal length of arithmetic progressions in $E$. Our main… read more here.
Keywords: self similar; similar sets; progressions self; arithmetic progressions ... See more keywords
Weak Self-Similar Sets in Separable Complete Metric Spaces
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DOI: 10.1142/s0218348x17500219
Abstract: Self-similarity is a common tendency in nature and physics. It is wide spread in geo-physical phenomena like diffusion and iteration. Physically, an object is self-similar if it is invariant under a set of scaling transformation.… read more here.
Keywords: self similar; similar sets; super self; weak self ... See more keywords
Thick self similar sets are asymptotically generic
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DOI: 10.5186/aasfm.2018.4349
Abstract: This paper studies the property of thickness for a class of self-similar sets that satisfy a non overlapping condition introduced by Strichartz. We show that in a suitable sense thickness is a generic property. read more here.
Keywords: self similar; similar sets; sets asymptotically; thick self ... See more keywords