The Assouad dimension of randomly generated fractals
| Autor: | Sascha Troscheit, Jonathan M. Fraser, Jun Jie Miao |
|---|---|
| Přispěvatelé: | University of St Andrews. Pure Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
28A80 60J80 37C45 54E52 82B43 Assouad dimension General Mathematics T-NDAS Structure (category theory) Dynamical Systems (math.DS) Mandelbrot set 01 natural sciences math.PR Baire category 010305 fluids & plasmas Fractal Mathematics - Metric Geometry Dimension (vector space) 0103 physical sciences math.GN FOS: Mathematics Mathematics::Metric Geometry QA Mathematics Mathematics - Dynamical Systems 0101 mathematics Self-similar set QA Mathematics - General Topology Mathematics Mandelbrot percolation Computer Science::Information Retrieval Applied Mathematics math.MG 010102 general mathematics Probability (math.PR) Hausdorff space General Topology (math.GN) Metric Geometry (math.MG) Random fractal Packing dimension Percolation Sample space Self-affine carpet Mathematics - Probability math.DS |
| Zdroj: | Fraser, J M, Miao, J J & Troscheit, S 2016, ' The Assouad dimension of randomly generated fractals ', Ergodic Theory and Dynamical Systems . https://doi.org/10.1017/etds.2016.64 BASE-Bielefeld Academic Search Engine |
| DOI: | 10.1017/etds.2016.64 |
| Popis: | We consider several different models for generating random fractals including random self-similar sets, random self-affine carpets, and fractal percolation. In each setting we compute either the \emph{almost sure} or the \emph{Baire typical} Assouad dimension and consider some illustrative examples. Our results reveal a common phenomenon in all of our models: the Assouad dimension of a randomly generated fractal is generically as big as possible and does not depend on the measure theoretic or topological structure of the sample space. This is in stark contrast to the other commonly studied notions of dimension like the Hausdorff or packing dimension. Comment: 26 pages, 7 figures, v3 corrected error in the proof of Theorem 3.2 and sharpened results on exceptional sets |
| Databáze: | OpenAIRE |
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