Quantifying inhomogeneity in fractal sets
Date
04/2018Metadata
Show full item recordAbstract
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the ‘most difficult location and scale’ at which to cover the set and its difference from box dimension can be thought of as a first-level overall measure of how inhomogeneous the set is. For the next level of analysis, we develop a quantitative theory of inhomogeneity by considering the measure of the set of points around which the set exhibits a given level of inhomogeneity at a certain scale. For a set of examples, a family of ( ×m, ×n )-invariant subsets of the 2-torus, we show that this quantity satisfies a Large Deviations Principle. We compare members of this family, demonstrating how the rate function gives us a deeper understanding of their inhomogeneity.
Citation
Fraser , J & Todd , M J 2018 , ' Quantifying inhomogeneity in fractal sets ' , Nonlinearity , vol. 31 , no. 4 , pp. 1313-1330 . https://doi.org/10.1088/1361-6544/aa9ee6
Publication
Nonlinearity
Status
Peer reviewed
ISSN
0951-7715Type
Journal article
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