Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-20T04:23:19.968Z Has data issue: false hasContentIssue false
  • English
  • Français

Box dimension for graphs of fractal functions

Published online by Cambridge University Press:  20 January 2009

Gavin Brown  and
Qinghe Yin
Gavin Brown
Affiliation:
Office of Vice Chancellor, The University of Sydney, Sydney, NSW 2006, AustraliaE-mail addresses:gavin@vcc.usyd.edu.au
Qinghe Yin
Affiliation:
Department of Pure Mathematics, The University of Adelaide, Adelaide, SA 5005, AustraliaE-mail addresses:qyin@spam.maths.adelaide.edu.au
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.

We calculate the box-dimension for a class of nowhere differentiable curves defined by Markov attractors of certain iterated function systems of affine maps.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 331 - 344
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1. Bedford, T., The Box Dimension of Self-affine Graphs And Repellers, Nonlinearity 2 (1989), 53–71.Google Scholar
2. Bush, K. A., Continuous Functions without Derivatives, Amer. Math. Monthly 59 (1952), 222–225.CrossRefGoogle Scholar
3. Ellis, D. B. and Branton, M. G., Non-self-similar Attractors of Hyperbolic Iterated Function Systems (Lecture Notes in Math., Vol 1342, Springer-Verlag, 1987), 158–171.CrossRefGoogle Scholar
4. Falconer, K. J., Bounded Distortion and Dimension for Non-conformal Repellers, Math. Proc. Cambridge Philos. Soc. 115 (1994), 315–334.CrossRefGoogle Scholar
5. Gibert, S. and Massopust, P. R., The Exact Hausdorff Dimension for a Class of Fractal Functions, J. Math. Anal. Appl. 168 (1992), 171–183.Google Scholar
6. Yin, Q., On Hausdorff Dimension for Attractors of Iterated Function Systems, J.Australian Math. Soc. Ser. A 55 (1993), 216–231.CrossRefGoogle Scholar