Bibliography for the Lorenz Attractor

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  1. Symbolic dynamics and periodic orbits of the Lorenz attractor
    Viswanath, D.
    Nonlinearity, 2003, vol. 16, no. 3, pp. 1035-1056, Ingenta.  
  2. Neural reconstruction of Lorenz attractors by an observable.
    Cannas, B.; Cincotti, S.
    Chaos Solitons Fractals 14 (2002), no. 1, 81--86, MathSciNet.
  3. A New View of the Lorenz Attractor
    Magnitskii, N. A.; Sidorov, S. V.
    Differential Equations, 2001, vol. 37, no. 11, pp. 1568-1579, Ingenta.  
  4. What's new on Lorenz strange attractors?  
    Viana, Marcelo
    Math. Intelligencer 22 (2000), no. 3, 6--19, MathSciNet.
  5. Mathematics: The Lorenz attractor exists  
    Stewart, Ian
    Nature, 2000, vol. 406, no. 6799, pp. 948, Ingenta.  
  6. Feasibility study of extended range atmospheric prediction through time average Lorenz attractor.
    Pal, Pradip K.; Shah, Shivani
    Indian journal of radio & space physics, 1999, vol. 28, no. 6, pp. 271, Ingenta.  
  7. Chaos and Peak-to-Peak Dynamics in a Plankton-Fish Model
    Sergio Rinaldi, Cosimo Solidoro
    Theoretical Population Biology, Vol. 54, No. 1, Aug 1998, pp. 62-77, Ideal.  
  8. Integrals of motion and the shape of the attractor for the Lorenz model.
    Giacomini, H.; Neukirch, S.
    Phys. Lett. A 227 (1997), no. 5-6, 309--318, MathSciNet.
  9. Spatial Chaotic Structure of Attractors of Reaction-Diffusion Systems  
    V. Afraimovich, A. Babin, S.-N. Chow  
    Transactions of the American Mathematical Society, Vol. 348, No. 12. (Dec., 1996), pp. 5031-5063, Jstor.  
  10. Bifurcation Structure of Lorenz-Type Five-Equation Model in Thermal Convection.
    Ilda, Sei-ichi; Ogawara, Kakuji
    JSME international journal. Series II, Fluids engineering, heat transfer, power, combustion, thermophysical properties, 1996, vol. 39, no. 1, pp. 36, Ingenta.  
  11. On the Strange Attractor and Transverse Homoclinic Orbits for the Lorenz Equations
    H. Spreuer, E. Adams
    Journal of Mathematical Analysis and Applications, Vol. 190, No. 2, Mar 1995, pp. 329-360, Ideal.
  12. Nonlinear Forecasting of Non-Uniform Chaotic Attractors in an Enzyme Reaction  
    L. F. Olsen, K. R. Valeur, T. Geest, C. W. Tidd, W. M. Schaffer  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 348, No. 1688, Chaos and Forecasting. (Sep. 15, 1994), pp. 421-430, Jstor.
  13. Ensembles of the Lorenz Attractor  
    A. P. Rothmayer, D. W. Black  
    Proceedings: Mathematical and Physical Sciences, Vol. 441, No. 1912. (May 8, 1993), pp. 291-312, Jstor.  
  14. New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High r in the Lorenz Equations  
    Jibin Li, Jianming Zhang  
    SIAM Journal on Applied Mathematics, Vol. 53, No. 4. (Aug., 1993), pp. 1059-1071, Jstor.  
  15. Chaos in Ecology: Is Mother Nature a Strange Attractor?  
    Alan Hastings, Carole L. Hom, Stephen Ellner, Peter Turchin, H. Charles J. Godfray  
    Annual Review of Ecology and Systematics, Vol. 24. (1993), pp. 1-33, Jstor.  
  16. On the multifractal character of the Lorenz attractor.
    Domínguez-Tenreiro, R.; Roy, L. J.; Martínez, V. J.
    Progr. Theoret. Phys. 87 (1992), no. 5, 1107--1118, Math. Sci. Net.
  17. Dissipative hydrodynamic oscillators. VII. The two-component Lorenz model as a Duffing oscillator, and integrability.
    Sanjuán, M. A. F.; Valero, J. L.; Velarde, M. G.
    Nuovo Cimento D (1) 13 (1991), no. 7, 913--918, MathSciNet.
  18. Attractor properties of laser dynamics: a comparison of NH3-laser emission with the Lorenz model.
    Li, M.Y.; Win, T.; Weiss, C.O.
    Optics communications, 1990, vol. 80, no. 2, pp. 119, Ingenta.  
  19. A Note on the Differential Equations of Gleick-Lorenz  
    Morris W. Hirsch  
    Proceedings of the American Mathematical Society, Vol. 105, No. 4. (Apr., 1989), pp. 961-962, Jstor.  
  20. Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics  
    Celso Grebogi, Edward Ott, James A. Yorke  
    Science, New Series, Vol. 238, No. 4827. (Oct. 30, 1987), pp. 632-638, Jstor.  
  21. Lorenz cross sections of the chaotic attractor of the double rotor.
    Kostelich, Eric J.; Yorke, James A.
    Phys. D 24 (1987), no. 1-3, 263--278, MathSciNet.
  22. Strange Attractors of Uniform Flows  
    Ittai Kan  
    Transactions of the American Mathematical Society, Vol. 293, No. 1. (Jan., 1986), pp. 135-159, Jstor.  
  23. On the Nature of the Torus in the Complex Lorenz Equations  
    A. C. Fowler, M. J. McGuinness  
    SIAM Journal on Applied Mathematics, Vol. 44, No. 4. (Aug., 1984), pp. 681-700, Jstor.  
  24. Intermediate model solutions to the Lorenz equations: strange attractors and other phenomena.
    Gent, Peter R.; McWilliams, James C.
    J. Atmospheric Sci. 39 (1982), no. 1, 3--13, MathSciNet.
  25. Ordinary Differential Equations with Strange Attractors  
    C. J. Marzec, E. A. Spiegel  
    SIAM Journal on Applied Mathematics, Vol. 38, No. 3. (Jun., 1980), pp. 403-421, Jstor.  
  26. Periodic Solutions and Bifurcation Structure at High R in the Lorenz Model  
    K. A. Robbins  
    SIAM Journal on Applied Mathematics, Vol. 36, No. 3. (Jun., 1979), pp. 457-472, Jstor.  
  27. New interpretation and size of strange attractor of the Lorenz model of turbulence.
    Haken, H.; Wunderlin, A.
    Phys. Lett. A 62 (1977), no. 3, 133--134, MathSciNet.
  28. Computer pictures of the Lorenz attractor.
    Lanford, Oscar E., III
    Turbulence Seminar (Univ. Calif., Berkeley, Calif., 1976/1977), pp. 113--116. Lecture Notes in Math., Vol. 615, Springer, Berlin, 1977, MathSciNet.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004