JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 53-58.doi: 10.6040/j.issn.1671-9352.0.2015.186

Previous Articles     Next Articles

Besicovitch-Eggleston type sets in cellular automata

PENG Tao-tao, LIU Wei-bin   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
  • Received:2015-04-23 Online:2016-04-20 Published:2016-04-08

Abstract: Consider a class of Besicovitch-Eggleston type sets associated cellular automata. Hausdorff dimensions of these sets are determined by tranforming them into some shift dynamics.

Key words: cellular automata, Hausdorff dimension, symbolic space

CLC Number: 

  • O174.12
[1] WALTERS P. An introduction to Ergodic theory[M] // Graduate Texts in Mathematics. New York: Springer, 2000.
[2] BESICOVITCH A S. On the sum of digits of real numbers represented in the dyadic system[J]. Mathematische Annalen, 1935, 110(1):321-330.
[3] EGGLESTON H G. The fractional dimension of a set defined by decimal properties, quarterly[J]. Journal of Mathematics Oxford Series, 1949, 47:31-40.
[4] XIE Y, WEN Z. Dimensions of modified Besicovitch-Eggleston sets[J]. Science in China, 2006, 49(2):245-254.
[5] 文志英. 分形几何的数学基础[M]. 上海:上海科技教育出版社,2000. WEN Zhiying. Mathematical foundation of fractal geometry[M]. Shanghai: Shanghai Scientific and Technological Education Publishing House, 2000.
[6] SHERESHEVSKY M A. Ergodic properties of certain surjective cellular automata[J]. Monatshefte Für Mathematik, 1992, 114(3-4):305-316.
[7] HEDLUND G A. Endomorphisms and automorphisms of the shift dynamical system[J]. Mathematical Systems Theory, 1969, 3(4):320-375.
[8] LIND Douglas, MARCUS Brian. An introduction to symbolic dynamics and coding[M]. Cambridge: Cambridge University Press, 1995.
[1] LI Wang,SUN Yong-zheng, . Cellular automata based simulation of new product market diffusion [J]. J4, 2008, 43(3): 92-96 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!