Skip to main content
SpringerLink
Log in

On the Hausdorff dimension of fractal attractors

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We consider such mappingsx n+1=F(xn) of an interval into itself for which the attractor is a Cantor set. For the same class of mappings for which the Feigenbaum scaling laws hold, we show that the Hausdorff dimension of the attractor is universally equal toD=0.538 ...

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Ruelle and F. Takens,Commun. Math. Phys. 20:167 (1971); S. Newhouse, D. Ruelle, and F. Takens,Commun. Math. Phys. 64:35 (1978).

    Google Scholar 

  2. B. B. Mandelbrot,Fractals: Form, Chance, and Dimension (Freeman, San Francisco, 1977).

    Google Scholar 

  3. H. Mori,Progr. Theor. Phys. 63:1044 (1980); H. Mori and H. Fujisaka,Progr. Theor. Phys. 63:1931 (1980).

    Google Scholar 

  4. D. A. Russell, J. D. Hanson, and E. Ott,Phys. Rev. Lett. 45:1175 (1980).

    Google Scholar 

  5. M. J. Feigenbaum,J. Stat. Phys. 19:25 (1978).

    Google Scholar 

  6. M. J. Feigenbaum,J. Stat. Phys. 21:669 (1979).

    Google Scholar 

  7. R. May and G. F. Oster,Am. Nat. 110:573 (1976).

    Google Scholar 

  8. V. Francheschini and C. Tebaldi,J. Stat. Phys. 21:707 (1979); V. Francheschini,J. Stat. Phys. 22:397 (1980).

    Google Scholar 

  9. A. Libchaber and J. Maurer,J. Phys. Lett. (Paris) 40:L419 (1979), and to be published.

    Google Scholar 

  10. P. Coullet and C. Tresser,C.R. Acad. Sci. Paris 287A:577 (1978);J. Phys. (Paris) 41:L255 (1980).

    Google Scholar 

  11. B. Derrida, A. Gervois, and Y. Pomeau,J. Phys. 12A:262 (1979).

    Google Scholar 

  12. P. Collet, J.-P. Eckmann, and O. E. Lanford III,Commun. Math. Phys. 76:211 (1980).

    Google Scholar 

  13. K. Konishi, preprint CERN-TH 2853 (1980).

  14. P. Grassberger and M. Scheunert, to be published inJ. Stat. Phys.

Download references

Author information

Authors and Affiliations

  1. Physics Department, University of Wuppertal, Wuppertal, Germany

    P. Grassberger

Authors
  1. P. Grassberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grassberger, P. On the Hausdorff dimension of fractal attractors. J Stat Phys 26, 173–179 (1981). https://doi.org/10.1007/BF01106792

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01106792

Key words

Search

Navigation