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The Assouad dimension of self-affine carpets with no grid structure
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dc.contributor.author | Fraser, Jonathan M. | |
dc.contributor.author | Jordan, Thomas | |
dc.date.accessioned | 2017-01-06T16:30:11Z | |
dc.date.available | 2017-01-06T16:30:11Z | |
dc.date.issued | 2017-06-16 | |
dc.identifier | 248514258 | |
dc.identifier | c92f50a7-52dc-430a-8a6d-bbe571830839 | |
dc.identifier | 85029572940 | |
dc.identifier | 000409193700029 | |
dc.identifier.citation | Fraser , J M & Jordan , T 2017 , ' The Assouad dimension of self-affine carpets with no grid structure ' , Proceedings of the American Mathematical Society , vol. 145 , pp. 4905-4918 . https://doi.org/10.1090/proc/13629 | en |
dc.identifier.issn | 0002-9939 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285457 | |
dc.identifier.uri | https://hdl.handle.net/10023/10061 | |
dc.description | JMF is financially supported by a Leverhulme Trust Research Fellowship. | en |
dc.description.abstract | Previous study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of self-affine carpets which do not have an associated grid structure. We find that the Assouad dimension is related to the box and Assouad dimensions of the (self-similar) projection of the self-affine set onto the first coordinate and to the local dimensions of the projection of a natural Bernoulli measure onto the first coordinate. In a special case we relate the Assouad dimension of the Przytycki-Urbański sets to the lower local dimensions of Bernoulli convolutions. | |
dc.format.extent | 293496 | |
dc.language.iso | eng | |
dc.relation.ispartof | Proceedings of the American Mathematical Society | en |
dc.subject | Assouad dimension | en |
dc.subject | Self-affine carpet | en |
dc.subject | Local dimension | en |
dc.subject | Bernoulli | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | The Assouad dimension of self-affine carpets with no grid structure | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1090/proc/13629 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RF-2016-500 | en |
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