Geodesic
More Variations on the Sierpiński Sieve
Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 543-562

Voir la notice de l'article provenant de la source Cambridge University Press

This paper answers a question of Broomhead, Montaldi and Sidorov about the existence of gaskets of a particular type related to the Sierpiński sieve. These gaskets are given by iterated function systems that do not satisfy the open set condition. We use the methods of Ngai and Wang to compute the dimension of these gaskets.
DOI : 10.4153/CJM-2010-036-3
Mots-clés : 28A80, 28A78, 11R06 
Hare, Kevin G. More Variations on the Sierpiński Sieve. Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 543-562. doi: 10.4153/CJM-2010-036-3
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[1] [1] Broomhead, D., Montaldi, J., and Sidorov, N., Golden gaskets: variations on the Sierpiński sieve. Nonlinearity 17(2004), no. 4, 1455–1480. doi: 10.1088/0951-7715/17/4/017 Google Scholar

[2] [2] Falconer, K., Techniques in Fractal Geometry. John Wiley & Sons, Chichester, 1997. Google Scholar

[3] [3] Falconer, K., Fractal Geometry. Mathematical Foundations and Applications. Second edition. John Wiley & Sons, Hoboken, NJ, 2003. Google Scholar

[4] [4] Hare, K. G.. Home page. http://www.math.uwaterloo.ca/-kghare, 2004. Google Scholar

[5] [5] Hutchinson, J. E., Fractals and self-similarity. Indiana Univ. Math. J. 30(1981), no. 5, 713–747. doi: 10.1512/iumj.1981.30.30055 Google Scholar

[6] [6] Lalley, S. P., -expansions with deleted digits for Pisot numbers . Trans. Amer. Math. Soc. 349(1997), no. 11, 4355–4365. doi: 10.1090/S0002-9947-97-02069-2 Google Scholar

[7] [7] Ngai, S.-M. and Wang, Y., Hausdorff dimension of self-similar sets with overlaps. J. London Math. Soc. 63(2001), no. 3, 655–672. doi: 10.1017/S0024610701001946 Google Scholar

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