Nonlinear dynamical systems may show irregular time development. Examples are fluids at the transition to turbulence, chemical reactions, the magnetic field of the earth, etc. The frequency spectrum is continuous and thus time correlations decay. Despite deterministic equations of motion the future development cannot be predicted due to instabilities against small disturbances. Some aspects of the motion are pseudo-random. Chaos turns out to be a dynamical quality besides the well-known exponential growth or the approach to a steady state.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Matthews, S.W.: Readers Digest Mai 1977, S. 39 (National Geographic, Nov. 1976)Google Scholar
  2. 2.
    Flohn, H.: Naturwissenschaften 66, 325 (1979)CrossRefGoogle Scholar
  3. 3.
    Olsen, L.F., Degn, H.: Nature 267, 177 (1977)PubMedCrossRefGoogle Scholar
  4. 4.
    Bullard, E., in: AIP Conf. Proc., La Jolla Inst., Ed. Siebe Jorna, Topics in Nonlinear Dynamics, AIP, 1978, p. 373CrossRefGoogle Scholar
  5. 5.
    Ahlers, G., in: Fluctuations, Instabilities, and Phase Transitions, p. 181. Proc. Geilo Conf. (ed. Riste, T.). New York: Plenum 1976Google Scholar
  6. 6.
    Taylor, G.I.: Phil. Trans. R. Soc. (Lond.) A 223, 289 (1923)CrossRefGoogle Scholar
  7. 7.
    Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon 1961Google Scholar
  8. 8.
    Bénard, H.: Rev. Gen. Sci. Pures Appl. 11, 1261 (1900)Google Scholar
  9. 8a.
    Rayleigh, Lord: Phil. Mag. J. Sci. 32, 529 (1916)CrossRefGoogle Scholar
  10. 9.
    Übersicht für das Taylor-System siehe: Koschmieder, E.L.: Adv. Chem. Phys. 32, 109 (1975); J. Fluid Mech. 93, 515 (1979)Google Scholar
  11. 10.
    Übersicht für das Rayleigh-Bénard-System siehe: Whitehead Jr., J.A., in: [5], p. 153Google Scholar
  12. 11.
    Swinney, H.L., Fenstermacher, P.R., Gollub, J.P., in: Synergetics, p. 60 (ed. Haken, H.). Berlin: Springer 1977CrossRefGoogle Scholar
  13. 12.
    Swinney, H.L., Gollub, J.P.: Phys. Today, August 1978, p. 41 13.Google Scholar
  14. 12a.
    Ahlers, G.: Phys. Rev. Lett. 33, 1185 (1974)CrossRefGoogle Scholar
  15. 12b.
    Ahlers, G, Waiden, R.W.: ibid. 44, 445 (1980)CrossRefGoogle Scholar
  16. 14.
    Gollub, J.P., Benson, S.V.: ibid. 41, 948 (1978)CrossRefGoogle Scholar
  17. 15.
    Ahlers, G., Behringer, R.P.: Progr. Theor. Phys. Suppl. 64, 190 (1978)CrossRefGoogle Scholar
  18. 16.
    Lorenz, E.N.: J. Atm. Sci. 20, 448 (1963)CrossRefGoogle Scholar
  19. 17.
    Grossmann, S., Sonneborn-Schmick, B.: Dynamische Korrelationen im Lorenzmodell (in Vorbereitung)Google Scholar
  20. 18.
    Larochelle, A., in: Internationale Rundfunk-Universität, HR, 2.7.1980Google Scholar
  21. 19.
    Robbins, K.A.: Math. Proc. Camb. Phil. Soc. 82, 309 (1977)CrossRefGoogle Scholar
  22. 20.
    Grossmann, S., Thomae, S.: Z. Naturforsch. 32a, 1353 (1977)Google Scholar
  23. 21.
    May, R.M.: Nature 261, 459 (1976)PubMedCrossRefGoogle Scholar
  24. 22.
    Berry, M.V.: AIP Conf. La Jolla, Ed. Siebe Jorna, Topics in Nonlinear Dynamics, AIP, New York 1978, p. 16Google Scholar
  25. 23.
    Moser, J.: Nachr. Akad. Wiss. Göttingen, IL Math. Physik. Kl. 1 (1962)Google Scholar
  26. 23a.
    Arnold, V.I.: Russian Math. Surv. 18, 85 (1963)CrossRefGoogle Scholar
  27. 23b.
    Moser, J.: Stable and Random Motions in Dynamical Systems. Princeton Univ. Press 1973Google Scholar
  28. 23c.
    Arnold, V.I., Avez, A.: Ergodic Problems in Classical Mechanics. New York-Amsterdam: Benjamin 1968Google Scholar
  29. 24.
    Born, M.: Usp. Fiz. Nauk 69, 2 (1959)Google Scholar
  30. 24a.
    Rabinovich, M.I.: Sov. Phys. Usp. 21, 443 (1978)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • S. Grossmann
    • 1
  1. 1.Fachbereich Physik der UniversitätMarburg/LahnDeutschland

Personalised recommendations