Skip to main content
Log in

The transition to aperiodic behavior in turbulent systems

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Some systems achieve aperiodic temporal behavior through the production of successive half subharmonics. A recursive method is presented here that allows the explicit computation of this aperiodic behavior from the initial subharmonics. The results have a character universal over specific systems, so that all such transitions are characterized by noise of a universal internal similarity.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Franceschini, V., Tebaldi, C.: Sequences of infinite bifurcation and turbulence in five-modes truncation of the Navier-Stokes equations. Istituto Matematico, Univ. di Modena preprint

  2. Franceschini, V.: A Feigenbaum sequence of bifurcations in the Lorenz model, Istituto Matematico, Univ. di Modena preprint, to be published in J. Stat. Phys.

  3. Computations by the author on Duffing's equation, following Ueda, Y.: J. Stat. Phys.20 (2), 181 (1979)

    Google Scholar 

  4. Holmes, P.: A nonlinear oscillator with a strange attractor. Department of Theoretical and Applied Mechanics, Cornell University (preprint)

  5. Huberman, B., Crutchfield, J.: Chaotic states of anharmonic systems in periodic fields. Xerox Corp., Palo Alto Research Center (preprint)

  6. Marzec, C.J., Spiegel, E.A.: A strange attractor. Astronomy Department, Columbia University (preprint)

  7. Libchaber, A., Maurer, J.: Une expérience de Rayleigh-Bénard de géométrie réduite. École Normale Supérieure (preprint)

  8. Feigenbaum, M.J.: Phys. Lett.74A, 375 (1979)

    Google Scholar 

  9. Collet, P., Eckmann, J.-P., Koch, H.: Period doubling bifurcations for families of maps onC n. Department of Physics, Harvard University (preprint)

  10. Metropolis, N., Stein, M.L., Stein, P.R.: Combinatorial Theory15 (1), 25 (1973)

    Google Scholar 

  11. May, R., Oster, G.: Amer. Naturalist110 (974), 573 (1976). This paper independently of myself, discovers the first clue of a universal metric property

    Google Scholar 

  12. Feigenbaum, M.J.: Annual Report 1975–76, LA-6816-PR, Los Alamos

  13. Feigenbaum, M.J.: J. Stat. Phys.19 (1), 25 (1978)

    Google Scholar 

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

  15. Feigenbaum, M.J.: Lecture Notes in Physics93, 163 (1979)

    Google Scholar 

  16. Collet, P., Eckmann, J.-P., Lanford III, O.: Universal properties of maps on an interval (in preparation)

  17. Collet, P., Eckmann, J.-P.: Bifurcations et groupe de renormalisation. IHES/P/78/250 (preprint)

  18. Derrida, B., Gervois, A., Pomeau, Y.: J. Phys. A12, 269 (1979). This paper contains the first numerical observation of δ in a 2-dimensional map

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feigenbaum, M.J. The transition to aperiodic behavior in turbulent systems. Commun.Math. Phys. 77, 65–86 (1980). https://doi.org/10.1007/BF01205039

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01205039

Keywords

Navigation