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Quantifying inhomogeneity in fractal sets
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dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Todd, Michael John | |
dc.date.accessioned | 2019-02-20T00:32:59Z | |
dc.date.available | 2019-02-20T00:32:59Z | |
dc.date.issued | 2018-04 | |
dc.identifier | 229614912 | |
dc.identifier | c9459ccd-e0f2-4067-b0b5-6035b319fbfb | |
dc.identifier | 85042311247 | |
dc.identifier | 000425666300002 | |
dc.identifier.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 | en |
dc.identifier.issn | 0951-7715 | |
dc.identifier.other | ORCID: /0000-0002-0042-0713/work/54181513 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285485 | |
dc.identifier.uri | https://hdl.handle.net/10023/17098 | |
dc.description.abstract | 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. | |
dc.format.extent | 437444 | |
dc.language.iso | eng | |
dc.relation.ispartof | Nonlinearity | en |
dc.subject | Large deviations | en |
dc.subject | Assouad dimension | en |
dc.subject | Box dimension | en |
dc.subject | Self-affine carpet | en |
dc.subject | QA Mathematics | en |
dc.subject | NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Quantifying inhomogeneity in fractal sets | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1088/1361-6544/aa9ee6 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2019-02-20 |
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