St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

The visible part of plane self-similar sets

Thumbnail
View/Open
FalconerProcAmMathSoc2012VisiblePart.pdf (505.6Kb)
Date
2013
Author
Falconer, Kenneth John
Fraser, Jonathan Macdonald
Keywords
Metric Geometry
QA Mathematics
Metadata
Show full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
Abstract
Given a compact subset F of R2, the visible part VθF of F from direction θ is the set of x in F such that the half-line from x in direction θ intersects F only at x. It is suggested that if dimH F ≥ 1 then dimH VθF = 1 for almost all θ , where dimH denotes Hausdorff dimension. We conrm this when F is a self-similar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval. In particular the underlying similarities may involve arbitrary rotations and F need not be connected.
Citation
Falconer , K J & Fraser , J M 2013 , ' The visible part of plane self-similar sets ' , Proceedings of the American Mathematical Society , vol. 141 , no. 1 , pp. 269-278 . https://doi.org/10.1090/S0002-9939-2012-11312-7
Publication
Proceedings of the American Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1090/S0002-9939-2012-11312-7
ISSN
0002-9939
Type
Journal article
Rights
© Copyright 2012 American Mathematical Society. First published in Proceedings of the American Mathematical Society 2012, published by the American Mathematical Society)
Description
JMF was supported by an EPSRC grant whilst undertaking this work.
Collections
  • University of St Andrews Research
URL
http://arxiv.org/pdf/1004.5067.pdf
URI
http://hdl.handle.net/10023/2756

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter