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On the Hausdorff Dimension of Graphs and Random Recursive Objects

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Dimensions and Entropies in Chaotic Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 32))

Abstract

The purpose of this note is to present some recent results and techniques concerning the Hausdorff dimension of various objects. We will report on an estimate for the lower bound of the dimension of a wide class of graphs which includes the Weierstrass-Hardy-Mandelbrot functions, and also on the exact dimension of some objects constructed via random recursions.

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References

  1. Rogers, C. A., Hausdorff Measures. Cambridge University Press, 1970.

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Author information

Authors and Affiliations

  1. Department of Mathematics, North Texas State University, P.O. Box 5116, Denton, TX, 76203, USA

    R. D. Mauldin

Authors
  1. R. D. Mauldin
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Editor information

Editors and Affiliations

  1. Center for Nonlinear Studies, Los Alamos National Laboratory, Mail Stop: B258, Los Alamos, NM, 87545, USA

    Gottfried Mayer-Kress

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© 1986 Springer-Verlag Berlin Heidelberg

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Mauldin, R.D. (1986). On the Hausdorff Dimension of Graphs and Random Recursive Objects. In: Mayer-Kress, G. (eds) Dimensions and Entropies in Chaotic Systems. Springer Series in Synergetics, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71001-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-71001-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71003-2

  • Online ISBN: 978-3-642-71001-8

  • eBook Packages: Springer Book Archive

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