Journal of Statistical Physics

, Volume 83, Issue 5–6, pp 1199–1210 | Cite as

The correlation functions near intermittency in a one-dimensional Piecewise parabolic map

  • H. Lustfeld
  • J. Bene
  • Z. Kaufmann
Short Communications

Abstract

Piecewise parabolic maps constitute a family of maps in the fully developed chaotic state and depending on a parameter that can be smoothly tuned to a weakly intermittent situation. Approximate analytic expressions are derived for the corresponding correlation functions. These expressions produce power-law decay at intermittency and a crossover from power-law decay to exponential decay below intermittency. It is shown that the scaling functions and the exponent of the power law depend on the kind of the correlations.

Key Words

Weak intermittency chaos phase transition correlation function scaling function crossover behavior critical slowing down 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Y. Pomeau and P. Manneville,Commun. Math. Phys. 74:189 (1980).Google Scholar
  2. 2.
    C. Grebogi, E. Ott, and J. A. Yorke,Phys. Rev. Lett. 48:1507 (1982).Google Scholar
  3. 3.
    C. Grebogi, E. Ott, F. J. Romeiras, and J. A. Yorke,Phys. Rev. A 36:5365 (1987).Google Scholar
  4. 4.
    N. Platt, E. A. Spiegel, and C. Tresser,Phys. Rev. Lett. 70:279 (1993).Google Scholar
  5. 5.
    A. Čenys and H. Lustfeld,J. Phys. A: Math. Gen. 29:11 (1996).Google Scholar
  6. 6.
    M. J. Feigenbaum, I. Procaccia, and T. Tel,Phys. Rev. A 39:5359 (1989).Google Scholar
  7. 7.
    S. Grossmann and H. Horner,Z. Phys. B 60:79 (1985).Google Scholar
  8. 8.
    G. Györgyi and P. Szépfalusy,Z. Phys. B 55:179 (1984).Google Scholar
  9. 9.
    P. Szépfalusy and G. Györgyi,Phys. Rev. A 33:2852 (1986).Google Scholar
  10. 10.
    A. Csordás and P. Szépfalusy,Phys. Rev. A 38:2582 (1988).Google Scholar
  11. 11.
    Z. Kaufmann, H. Lustfeld, and J. Bene,Phys. Rev. E 53:1416 (1996).Google Scholar
  12. 12.
    J. Bene, Z. Kaufmann, and H. Lustfeld, Preprint.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • H. Lustfeld
    • 1
  • J. Bene
    • 2
  • Z. Kaufmann
    • 2
  1. 1.Institut für FestkörperforschungForschungszentrum JülichJülichGermany
  2. 2.Institute for Solid State PhysicsEötvös UniversityBudapestHungary

Personalised recommendations