Weak separation condition, Assouad dimension, and Furstenberg homogeneity
| Autor: | Eino Rossi, Antti Käenmäki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
General Mathematics
Homogeneity (statistics) ta111 Open set Primary 28A80 Secondary 37C45 28D05 28A50 Moran construction iterated function system Set (abstract data type) Combinatorics Dimension (vector space) dimension Mathematics - Classical Analysis and ODEs weak separation condition Classical Analysis and ODEs (math.CA) FOS: Mathematics Limit (mathematics) Limit set Cluster analysis Real line Mathematics |
| Popis: | We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous. 22 pages, 2 figures |
| Databáze: | OpenAIRE |
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