Abstract
Let K be a statistically self-similar set defined by Graf. In this paper, we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with ρ. Under such a decomposition, we obtain the expression of the spectrum function ƒ(α).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Mandelbort, Negative fractal dimension and multifractals, Physics A, 1990, 163:306–315
R. Cawley, R. D. Mauldin, Multifractal decomposition of Moran fractals, Adv. Math., 1992, 92:196–236
K. J. Falconer, Random fractals, Math. Proc Camb. Phil Soc., 1987, 100:559–582
R. D. Mauldin, S. C. Williams, Random recursive constructions:asymptotic geometric and topological properties, Tran. Am. Math. Soc., 1986, 295:325–346
S. Graf, Statistically self-similar fractal, Prob. Theor. Rel. Fields, 1987, 74:357–392
K. J. Falconer, The multifractal spectrum of statistically self-similar measure, J. of Theor. Prob., 1994, 7(3):681–702
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by National Natural Science Foundation of China (No. 19671066)
Rights and permissions
About this article
Cite this article
Yu, J.H., Hu, D.H. Multifractal Decomposition of Statistically Self-Similar Sets. Acta Math Sinica 17, 507–516 (2001). https://doi.org/10.1007/s101140100121
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s101140100121