Tilings of limit spaces of self-similar groups |
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| Author |
ibond.univ@gmail.com
National Taras Shevchenko University of Kyiv
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| Abstract |
We consider tilings of limit spaces of self-similar groups and discuss the following problem:
when does the tile of a self-similar group admit a tiling of the limit space under the action of
a (self-similar) subgroup?
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| Keywords |
self-similar group; limit space; tiling; lattice tiling; self-affine tile
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| Reference |
1. I. Bondarenko, R. Kravchenko, Graph-directed systems and self-similar measures on limit spaces of selfsimilar
groups, Advances in Mathematics, 226 (2011), ¹3, 2169–2191.
2. J.-P. Conze, L. Herve, A. Raugi, Pavages auto-affines, operateur de transfert et crit‘eres de r’eseau dans $\mathbb{R}^d$, Bol. Soc. Brasil. Mat.(N.S.), 28 (1997), 1–42. 3. J.-P. Gabardo, X. Yu, Natural tiling, lattice tiling and Lebesgue measure of integral self-affine tiles, J. Lond. Math. Soc., II. Ser., 74 (2006), ¹1, 184–204. 4. K. Grochenig, A. Haas, Self-similar lattice tilings, Journal of Fourier Analysis and Applications, 1 (1994), ¹2, 131–170. 5. J.C. Lagarias, Y. Wang, Integral self-affine tiles in $\mathbb{R}^n$ II: Lattice tilings, Journal of Fourier Analysis and Applications, 3 (1997), ¹1, 83–102. 6. W. Lawton, Proof of the hyperplane zeros conjecture of Lagarias and Wang, Journal of Fourier Analysis and Applications, 14 (2008), ¹4, 588–605. 7. V. Nekrashevych, Self-similar groups, Mathematical Surveys and Monographs, V.117, AMS, Providence, RI, 2005. |
| Pages |
134-138
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| Volume |
41
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| Issue |
2
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| Year |
2014
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| Journal |
Matematychni Studii
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