Assouad dimensions of Moran sets

Jinjun Li

doi:10.1016/j.crma.2013.01.010

Mathematical Analysis

Assouad dimensions of Moran sets

Présenté par : the Editorial Board

Jinjun Li ¹

¹ Department of Mathematics, Zhangzhou Normal University, Zhangzhou, 363000, PR China

Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 19-22.

Résumé
Abstract

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 : 2012-10-17
Accepté le : 2013-01-21
Publié le : 2013-01-01

DOI : 10.1016/j.crma.2013.01.010

Affiliations des auteurs :

Jinjun Li ¹

¹ Department of Mathematics, Zhangzhou Normal University, Zhangzhou, 363000, PR China

@article{CRMATH_2013__351_1-2_19_0,
     author = {Jinjun Li},
     title = {Assouad dimensions of {Moran} sets},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {19--22},
     publisher = {Elsevier},
     volume = {351},
     number = {1-2},
     year = {2013},
     doi = {10.1016/j.crma.2013.01.010},
     language = {en},
}

TY  - JOUR
AU  - Jinjun Li
TI  - Assouad dimensions of Moran sets
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 19
EP  - 22
VL  - 351
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crma.2013.01.010
LA  - en
ID  - CRMATH_2013__351_1-2_19_0
ER  -

%0 Journal Article
%A Jinjun Li
%T Assouad dimensions of Moran sets
%J Comptes Rendus. Mathématique
%D 2013
%P 19-22
%V 351
%N 1-2
%I Elsevier
%R 10.1016/j.crma.2013.01.010
%G en
%F CRMATH_2013__351_1-2_19_0

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/

Bibliographie
Cité par

[1] P. Assouad Plongements lischitziens dans $R^{n}$ , Bull. Soc. Math. France, Volume 111 (1983), pp. 429-448

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

[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

Xiao JiaQing; Carmelo Antonio Finocchiaro Assouad and Lower Dimensions of Some Homogeneous Cantor Sets, Journal of Mathematics, Volume 2022 (2022) no. 1 | DOI:10.1155/2022/3501228
JiaQing Xiao Assouad dimensions and lower dimensions of some Moran sets, Journal of Mathematics, Volume 2020 (2020), p. 5 (Id/No 8353591) | DOI:10.1155/2020/8353591 | Zbl:1489.28010
Wenwen Li; Wenxia Li; Junjie Miao; Lifeng Xi Assouad dimensions of Moran sets and Cantor-like sets, Frontiers of Mathematics in China, Volume 11 (2016) no. 3, pp. 705-722 | DOI:10.1007/s11464-016-0539-6 | Zbl:1364.28011

Cité par 3 documents. Sources : Crossref, zbMATH

Commentaires - Politique

Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !

Publier un nouveau commentaire:

Publier une nouvelle réponse: