Hostname: page-component-7dd5485656-kp629 Total loading time: 0 Render date: 2025-10-30T14:01:20.506Z Has data issue: false hasContentIssue false
  • English
  • Français

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: qrdeng@fjnu.edu.cn)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Information

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

[1] Bedford, T. and Fisher, A., ‘Analogues of the Lebesgue density theorem for fractal sets of reals and integers’, Proc. London Math. Soc. (3) 30 (1992), 95–124.CrossRefGoogle Scholar
[2] Ngai, S.-M. and Wang, Y., ‘Hausdorff dimension of self-similar sets with overlaps’, J. London Math. Soc. (2) 63 (2001), 655–672.CrossRefGoogle Scholar
[3] Nguyen, N., ‘Iterated function systems of finite type and the weak separation property’, Proc. Amer. Math. Soc. 130 (2002), 483–487.CrossRefGoogle Scholar
[4] Strichartz, R. S., ‘Fractal in large’, Canad. J. Math. 50 (1996), 638–657.CrossRefGoogle Scholar