Comptes Rendus
no. 1-2
Mathematical Analysis
Assouad dimensions of Moran sets

Présenté par : the Editorial Board

Jinjun Li1
1 Department of Mathematics, Zhangzhou Normal University, Zhangzhou, 363000, PR China
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 19-22.

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.

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.01.010
Jinjun Li 1

1 Department of Mathematics, Zhangzhou Normal University, Zhangzhou, 363000, PR China 
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Jinjun Li. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.010/

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

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

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

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

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

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

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

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

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

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

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