《Connectednessamp;#8203; of a Class ofPlanar Self-Affine Tiles》.pdf

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: /copyright Authors personal copy J. Math. Anal. Appl. 380 (2011) 493–500 Contents lists available at ScienceDirect Journal of Mathematical Analysis and Applications /locate/jmaa Connectedness of a class of planar self-affine tiles ✩ Qi-Rong Deng a,∗, Ka-sing Lau b a Department of Mathematics, Fujian Normal University, Fuzhou 350007, PR China b Department of Mathematics, The Chinese University of Hong Kong, Hong Kong a r t i c l e i n f o a b s t r a c t Article history: We consider a class of planar self-affine tiles T that are generated by the lower triangular Received 26 January 2010 expanding matrices and the product-form digit sets. We give necessary and sufficient Available online 23 March 2011