Strange attractors

  • Carles Perelló
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 164)


Periodic Orbit Periodic Point Strange Attractor Closed Orbit Stable Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    M.L. CARTWRIGHT, Almost periodic solutions of equations with periodic coefficients. In Nonlinear Problems, University of Wisconsin Press, 207–218 (1964).Google Scholar
  2. (2).
    N. LEVINSON, Transformation theory of nonlinear differential equations of the second order, Annals of Mathematics, 45, 723–737 (1944)Google Scholar
  3. (3).
    J.E. LITTLEWOOD, On van der Pol's equation with large k. Ibid (1), 161–165.Google Scholar
  4. (4).
    E.N. LORENZ, Deterministic nonperiodic flow. J. Atmos.Sci. 20, 130–141 (1963).Google Scholar
  5. (5).
    T. RIKITAKE, Proc. Cambridge Philos. Soc., 54, 89 (1958).Google Scholar
  6. (6).
    O.E. ROSSLER,“Different types of chaos in two simple differential equations”. Z. Naturforsch. 31a, 1664–1670 (1976).Google Scholar
  7. (7).
    D. HENRY, Geometric theory of semilinear parabolic equations. Lect. Notes in Math. 840 Springer-Verlag (1981).Google Scholar
  8. (8).
    D. RUELLE and F. TAKENS, On the nature of turbulence. Commun. Math. Phys. 20, 167–192 (1971).Google Scholar
  9. (9).
    O.A. LADYSHENSKAYA, The mathematical theory of viscous incompressible flow, Gordon and Breach (1963).Google Scholar
  10. (10).
    R.F. WILLIAMS, The Lorenz attractor. Lect. Notes in Math. 615. Springer-Verlag, 94–112 (1977)Google Scholar
  11. (11).
    Z. NITECKY, Differentiable dynamics. M.I.T. Press (1971).Google Scholar
  12. (12).
    D. RUELLE, The Lorenz attractor and the problem of turbulence. Lecture Notes in Math. 565. Springer-Verlag, 146–158 (1976).Google Scholar
  13. (13).
    J.E. MARSDEN, Attempts to relate the Navier-Stokes equations to turbulence. Lect. Notes in Math. 615, Springer-Verlag 1–22 (1977).Google Scholar
  14. (14).
    J.L. KAPLAN and J.A. YORKE, Preturbulence: a regime observed in a fluid flow model of Lorenz. Commun. Math. Phys. 67, 93–108 (1979).Google Scholar
  15. (15).
    J. GUCKENHEIMER, A strange strange attractor. In Marsden, J.E., McCracken, M. Hopf bifurcation and its applications, Springer-Verlag, 368–381 (1976).Google Scholar
  16. (16).
    R.F. WILLIAMS, The structure of Lorenz attractors. Preprint (1977).Google Scholar
  17. (17).
    C. PERELLO, Intertwining invariant manifolds and the Lorenz attractor, Lect. Notes in Math. 819, Springer-Verlag, 375–378 (1980)Google Scholar
  18. (18).
    A.E. COOK and P.N. ROBERTS, The Rikitake two-disc dynamo system. Proc. Cambridge Philos. Soc., 68, 547–569 (1970).Google Scholar
  19. (19).
    J. VALERO, El sistema de Rikitake. Actas III Congreso de Ecuaciones diferenciales y aplicaciones, Santiago de Compostela, 313–329, (1980).Google Scholar
  20. (20).
    O.E. ROSSLER, An equation for hyperchaos. Physics letters, 71A, 155–157 (1979).Google Scholar
  21. (21).
    O.E. ROSSLER, Chaotic behavior in simple reaction systems. Z. Naturforsch. 31a, 259–264 (1976).Google Scholar
  22. (22).
    C. BONET, Tesis de Llicenciatura. Facultat de Ciencies. Universitat Autònoma de Barcelona.Google Scholar
  23. (23).
    K. KIRCHGÄSSNER, and H. KIELHÖFER, Stability and bifurcation in fluid mechanics, Rocky Mtn. Math. J. 3, 275–318 (1973).Google Scholar
  24. (24).
    H.L. SWINNEY and J.P. GOLLUB, The transition to turbulence.Physics Today, August 1978, 41–49.Google Scholar
  25. (25).
    O.E. ROSSLER, The flueing-together principle in chaos. Innonlinear problems of analysis in geometry and mechanics, Research Notes in Math. 46. Pitman, 50–56 (1981).Google Scholar
  26. (26).
    R. MANE, Reduction of semilinear parabolic equations to finite d_i mensional C1 flows, Lect. Notes in Math. 597, 361–378 (1977).Google Scholar
  27. (27).
    X. MORA, Finite-dimensional attracting manifolds in reaction-diffu sion equations. University of Warwick Notes (1981).Google Scholar
  28. (28).
    A. CALSINA,Bifurcacions genèriques d'attractors en sistemes de reac ció idifusió. Publ.Secc. de Mat. 24, Barcelona,73–162 (1981)Google Scholar
  29. (29).
    X. MORA, Reaction diffusion equations define dynamical systems. University of Warwick Notes (1981).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Carles Perelló
    • 1
  1. 1.Facultat de Ciencies. Secció de MatemàtiquesUniversitat Autbnoma de BarcelonaBellaterra, BarcelonaSpain

Personalised recommendations