Mathematical Analysis
Assouad dimensions of Moran sets
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 19-22.

We prove that the Assouad dimensions of a class of Moran sets coincide with their upper box dimensions and packing dimensions.

Nous montrons que, pour les ensembles dʼune classe de Moran, la dimension dʼAssouad coïncide avec la dimension de boîte supérieure et avec la dimension dʼempilement.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.01.010
Li, Jinjun 1

1 Department of Mathematics, Zhangzhou Normal University, Zhangzhou, 363000, PR China
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Li, Jinjun. Assouad dimensions of Moran sets. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 19-22. doi : 10.1016/j.crma.2013.01.010. http://www.numdam.org/articles/10.1016/j.crma.2013.01.010/

[1] Assouad, P. Plongements lischitziens dans Rn, Bull. Soc. Math. France, Volume 111 (1983), pp. 429-448

[2] Falconer, K.J. Fractal Geometry: Mathematical Foundations and Applications, John Wiley and Sons, Ltd, Chichester, 1990

[3] Heinonen, J. Lectures on Analysis on Metric Spaces, Springer-Verlag, New York, 2001

[4] Hua, S.; Rao, H.; Wen, Z.Y.; Wu, J. On the structures and dimensions of Moran sets, Sci. China, Ser. A, Volume 43 (2000), pp. 836-852

[5] Hutchinson, J. Fractals and self-similarity, Indiana Univ. Math. J., Volume 30 (1981), pp. 713-747

[6] Luukkainen, J. Assouad dimension: Antifractal metrization, porous sets, and homogeneous measures, J. Korean Math. Soc., Volume 35 (1998), pp. 23-76

[7] Mackay, J.M. Assouad dimension of self-affine carpets, Conform. Geom. Dyn., Volume 15 (2011), pp. 177-187

[8] Olsen, L. On the Assouad dimension of graph directed Moran fractals, Fractals, Volume 19 (2011), pp. 221-226

[9] Tricot, C. Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc., Volume 91 (1982), pp. 57-74

[10] Tyson, J. Global conformal Assouad dimension in the Heisenberg group, Conform. Geom. Dyn., Volume 12 (2008), pp. 32-57

[11] Wen, Z.Y. Moran sets and Moran classes, Chin. Sci. Bull., Volume 46 (2001), pp. 1849-1856

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