Pollicott, Mark and Vytnova, Polina (2015) Estimating singularity dimension. Mathematical Proceedings of the Cambridge Philosophical Society, 158 (2). pp. 223-238. doi:10.1017/S030500411400053X ISSN 0305-0041.

Preview

PDF WRAP_sd12.pdf - Accepted Version - Requires a PDF viewer. Download (764Kb) | Preview

Request Changes to record.

Abstract

In this paper we address an interesting question on the computation of the dimension of self-affine sets in Euclidean space. A well-known result of Falconer showed that under mild assumptions the Hausdorff dimension of typical self-affine sets is equal to its Singularity dimension. Heuter and Lalley subsequently presented a smaller open family of non-trivial examples for which there is an equality of these two dimensions. In this article we analyse the size of this family and present an efficient algorithm for estimating the dimension.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hausdorff measures
Journal or Publication Title:	Mathematical Proceedings of the Cambridge Philosophical Society
Publisher:	Cambridge University Press
ISSN:	0305-0041
Official Date:	March 2015
Dates:	Date Event March 2015 Published 16 December 2014 Available 24 June 2014 Submitted
Volume:	158
Number:	2
Number of Pages:	17
Page Range:	pp. 223-238
DOI:	10.1017/S030500411400053X
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	9 June 2016
Date of first compliant Open Access:	10 June 2016
Adapted As:

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads