Files in this item
Assouad type dimensions of infinitely generated self-conformal sets
Item metadata
dc.contributor.author | Banaji, Amlan | |
dc.contributor.author | Fraser, Jonathan | |
dc.date.accessioned | 2024-03-01T11:30:06Z | |
dc.date.available | 2024-03-01T11:30:06Z | |
dc.date.issued | 2024-04 | |
dc.identifier | 299219845 | |
dc.identifier | cc19be86-e6af-4972-b8cb-8450a976e852 | |
dc.identifier | 85186343205 | |
dc.identifier.citation | Banaji , A & Fraser , J 2024 , ' Assouad type dimensions of infinitely generated self-conformal sets ' , Nonlinearity , vol. 37 , no. 4 , 045004 . https://doi.org/10.1088/1361-6544/ad2864 | en |
dc.identifier.issn | 0951-7715 | |
dc.identifier.other | ORCID: /0000-0002-3727-0894/work/154531560 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/154532359 | |
dc.identifier.uri | https://hdl.handle.net/10023/29397 | |
dc.description | Funding: Both authors were financially supported by a Leverhulme Trust Research Project Grant (RPG-2019-034). JMF was also supported by an EPSRC Standard Grant (EP/R015104/1) and an RSE Sabbatical Research Grant (70249). Most of this work was completed while AB was JMF’s PhD student at the University of St Andrews, but AB was also supported by an EPSRC New Investigators Award (EP/W003880/1) while a postdoc at Loughborough University. | en |
dc.description.abstract | We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of sets. Under natural separation conditions, we prove a formula for the Assouad dimension and prove sharp bounds for the Assouad spectrum in terms of the Hausdorff dimension of the limit set and dimensions of the set of fixed points of the contractions. The Assouad spectra of the family of examples which we use to show that the bounds are sharp display interesting behaviour, such as having two phase transitions. Our results apply in particular to sets of real or complex numbers which have continued fraction expansions with restricted entries, and to certain parabolic attractors. | |
dc.format.extent | 32 | |
dc.format.extent | 457209 | |
dc.language.iso | eng | |
dc.relation.ispartof | Nonlinearity | en |
dc.subject | Conformal iterated function system | en |
dc.subject | Assouad dimension | en |
dc.subject | Assouad spectrum | en |
dc.subject | Continued fractions | en |
dc.subject | Parabolic iterated function system | en |
dc.subject | T-DAS | en |
dc.title | Assouad type dimensions of infinitely generated self-conformal sets | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. University of St Andrews | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1088/1361-6544/ad2864 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.