Skip to main content
SpringerLink
Log in

The Complete Devil′s Staircase and Universality of Mode Locking Structures in Discrete Mappings

  • Chapter
Multicritical Phenomena

Part of the book series: NATO ASI Series ((NSSB,volume 106))

  • 138 Accesses

Abstract

We study mode locking in certain discrete mappings. The mode locking traces up a complete devil′s staircase of fractal dimension D ~ 0.87. This exponent is universal for a large class of functions and we expect to find similar behaviour in systems with two competing frequencies.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.J. Feigenbaum, J.Stat.Phys. 19:25 (1978); 21: 669 (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. S.J. Shenker, Physica5D: 405 (1982).

    MathSciNet  ADS  Google Scholar 

  3. M.J. Feigenbaum, L.P. Kadanoff and S. J. Shenker, Physica5D: 370 (1982).

    MathSciNet  ADS  Google Scholar 

  4. D. Rand, S. Ostlund, J. Sethna and E. Siggia, Phys.Rev.Lett. 49:132 (1982); S. Ostlund, D. Rand, J. Sethna and E. Siggia, Santa Barbara Preprint (1982).

    Article  MathSciNet  ADS  Google Scholar 

  5. V.N. Belykh, N.F. Pedersen and O.H. Soerensen, Phys.Rev.B16: 4860 (1977).

    Article  ADS  Google Scholar 

  6. M.R. Herman, Lecture Notes in Mathematics 597: 271 (1977).

    Article  MathSciNet  Google Scholar 

  7. M. Høgh Jensen, Per Bak and Tomas Bohr, H.C. Ørsted Institute Preprint (1983).

    Google Scholar 

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

    MATH  Google Scholar 

  9. A. Libchaber, private communication

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. H.C. Ørsted Institute, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark

    M. Høgh Jensen, Per Bak & Tomas Bohr

  2. Brookhaven National Laboratory, Upton, N.Y, 11973, USA

    Per Bak

Authors
  1. M. Høgh Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Per Bak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomas Bohr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut Laue-Langevin, Grenoble, France

    R. Pynn

  2. Institute for Energy Technology, Kjeller, Norway

    A. Skjeltorp

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Plenum Press, New York

About this chapter

Cite this chapter

Jensen, M.H., Bak, P., Bohr, T. (1984). The Complete Devil′s Staircase and Universality of Mode Locking Structures in Discrete Mappings. In: Pynn, R., Skjeltorp, A. (eds) Multicritical Phenomena. NATO ASI Series, vol 106. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2741-7_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-2741-7_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9698-0

  • Online ISBN: 978-1-4613-2741-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation