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Assouad type dimensions and homogeneity of fractals
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| dc.contributor.author | Fraser, Jonathan M. | |
| dc.date.accessioned | 2014-12-19T10:01:02Z | |
| dc.date.available | 2014-12-19T10:01:02Z | |
| dc.date.issued | 2014-12 | |
| dc.identifier | 159774260 | |
| dc.identifier | eb0a09d4-5aee-4f42-80db-6d006b653fa6 | |
| dc.identifier | 000344826300017 | |
| dc.identifier | 84908391921 | |
| dc.identifier | 000344826300017 | |
| dc.identifier.citation | Fraser , J M 2014 , ' Assouad type dimensions and homogeneity of fractals ' , Transactions of the American Mathematical Society , vol. 366 , no. 12 , pp. 6687-6733 . https://doi.org/10.1090/S0002-9947-2014-06202-8 | en |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285467 | |
| dc.identifier.uri | https://hdl.handle.net/10023/5941 | |
| dc.description | The author was supported by an EPSRC Doctoral Training Grant | en |
| dc.description.abstract | We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity. | |
| dc.format.extent | 47 | |
| dc.format.extent | 621984 | |
| dc.language.iso | eng | |
| dc.relation.ispartof | Transactions of the American Mathematical Society | en |
| dc.subject | Assouad dimension | en |
| dc.subject | Lower dimension | en |
| dc.subject | Self-affine carpet | en |
| dc.subject | Ahlfors regular | en |
| dc.subject | Measurability | en |
| dc.subject | Baire hierarchy | en |
| dc.subject | Self-similar sets | en |
| dc.subject | Hausdorff dimension | en |
| dc.subject | Packing dimension | en |
| dc.subject | Affine fractals | en |
| dc.subject | Spaces | en |
| dc.subject | QA Mathematics | en |
| dc.subject.lcc | QA | en |
| dc.title | Assouad type dimensions and homogeneity of fractals | en |
| dc.type | Journal article | en |
| dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
| dc.identifier.doi | 10.1090/S0002-9947-2014-06202-8 | |
| dc.description.status | Peer reviewed | en |
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