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Hausdorff dimension of random fractals with overlaps

Published online by Cambridge University Press:  17 April 2009

Z. G. Yu ,
V. V. Anh  and
K. S. Lau
Z. G. Yu
Affiliation:
Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia Department of Mathematics, Xiangtan University, Hunan 411105, Peoples Republic ov China
V. V. Anh
Affiliation:
Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
K. S. Lau
Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
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Abstract

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This paper considers random fractals generated by contractive transformations which satisfy a separation condition weaker than the open set condition. This condition allows overlaps in the iterations. Estimates of the Hausdorff dimension of this kind of random fractals are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 315 - 328
Copyright
Copyright © Australian Mathematical Society 2002

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