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dc.contributor.authorFraser, Jonathan
dc.contributor.authorTodd, Michael John
dc.date.accessioned2019-02-20T00:32:59Z
dc.date.available2019-02-20T00:32:59Z
dc.date.issued2018-04
dc.identifier229614912
dc.identifierc9459ccd-e0f2-4067-b0b5-6035b319fbfb
dc.identifier85042311247
dc.identifier000425666300002
dc.identifier.citationFraser , 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/aa9ee6en
dc.identifier.issn0951-7715
dc.identifier.otherORCID: /0000-0002-0042-0713/work/54181513
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285485
dc.identifier.urihttps://hdl.handle.net/10023/17098
dc.description.abstractAn 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.extent437444
dc.language.isoeng
dc.relation.ispartofNonlinearityen
dc.subjectLarge deviationsen
dc.subjectAssouad dimensionen
dc.subjectBox dimensionen
dc.subjectSelf-affine carpeten
dc.subjectQA Mathematicsen
dc.subjectNDASen
dc.subject.lccQAen
dc.titleQuantifying inhomogeneity in fractal setsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1088/1361-6544/aa9ee6
dc.description.statusPeer revieweden
dc.date.embargoedUntil2019-02-20


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