Assouad type dimensions and homogeneity of fractals
MetadataShow full item record
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.
Fraser , J M 2014 , ' Assouad type dimensions and homogeneity of fractals ' Transactions of the American Mathematical Society , vol 366 , no. 12 , pp. 6687-6733 . DOI: 10.1090/S0002-9947-2014-06202-8
Transactions of the American Mathematical Society
© Copyright 2014 American Mathematical Society. First published in Transactions of the American Mathematical Society in Volume 366 (2014), published by the American Mathematical Society. This version may be reproduced under a CC-BY-NC-ND Creative Commons Licence (https://creativecommons.org/licenses/by-nc-nd/4.0/)
DescriptionThe author was supported by an EPSRC Doctoral Training Grant
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Showing items related by title, author, creator and subject.
Farkas, Ábel (University of St Andrews, 2015-11-30) - ThesisWe introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any ...
Fraser, Jonathan M. (University of St Andrews, 2013-11-29) - ThesisThe aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention ...
An analytical, phenomenological and numerical study of geophysical and magnetohydrodynamic turbulence in two dimensions Blackbourn, Luke A. K. (University of St Andrews, 2013-11-29) - ThesisIn this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes ...