Skip Navigation

Journal of the London Mathematical Society 2000 62(1):291-304; doi:10.1112/S002461070000106X
© 2000 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kirat, I.
Right arrow Articles by Lau, K.-S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

On the Connectedness of Self-Affine Tiles

Ibrahim Kirat and Ka-Sing Lau

Department of Mathematics, University of Pittsburgh Pittsburgh, PA 15260, USA, ibkst+{at}pitt.edu
Department of Mathematics, Chinese University of Hong Kong Hong Kong, kslau{at}math.cuhk.edu.hk

Received 6 November 1998. Revision received 11 March 1999.

Let T be a self-affine tile in Rn defined by an integral expanding matrix A and a digit set D. The paper gives a necessary and sufficient condition for the connectedness of T. The condition can be checked algebraically via the characteristic polynomial of A. Through the use of this, it is shown that in R2, for any integral expanding matrix A, there exists a digit set D such that the corresponding tile T is connected. This answers a question of Bandt and Gelbrich. Some partial results for the higher-dimensional cases are also given.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.