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REVERSE ITERATED FUNCTION SYSTEM AND DIMENSION OF DISCRETE FRACTALS

Part of: Classical measure theory

Published online by Cambridge University Press:  09 February 2009

QI-RONG DENG
QI-RONG DENG*
Affiliation:
Department of Mathematics, Fujiaan Normal University, Fuzhou, 350007, People’s Republic of China (email: [email protected])
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Abstract

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A reverse iterated function system is defined as a family of expansive maps {T1,T2,…,Tm} on a uniformly discrete set . An invariant set is defined to be a nonempty set satisfying F=⋃ j=1mTj(F). A computation method for the dimension of the invariant set is given and some questions asked by Strichartz are answered.

Keywords

reverse iterated function systemdimensiondiscrete invariant setoverlap

MSC classification

Secondary: 28A80: Fractals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 37 - 47
Copyright
Copyright © Australian Mathematical Society 2009

References

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[4] Strichartz, R. S., ‘Fractal in large’, Canad. J. Math. 50 (1996), 638–657.CrossRefGoogle Scholar