Chaos - James Gleick [158]
THIS ASSUMPTION Ruelle; also “Turbulent Dynamical Systems,” p. 281.
TEXT ON FLUID DYNAMICS L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Oxford: Pergamon, 1959).
THE OSCILLATORY, THE SKEWED VARICOSE Malkus.
“THAT’S TRUE” Swinney.
IN 1973 SWINNEY Swinney, Gollub.
“IT WAS A STRING-AND–SEALING-WAX” Dyson.
“SO WE READ THAT” Swinney.
WHEN THEY BEGAN REPORTING Swinney, Gollub.
“THERE WAS THE TRANSITION” Swinney.
EXPERIMENT FAILED TO CONFIRM J. P. Gollub and H. L. Swinney, “Onset of Turbulence in a Rotating Fluid,” Physical Review Letters 35 (1975), p. 927. These first experiments only opened the door to an appreciation of the complex spatial behaviors that could be produced by varying the few parameters of flow between rotating cylinders. The next few years identified patterns from “corkscrew wavelets” to “wavy inflow and outflow” to “interpenetrating spirals.” A summary is C. David Andereck, S. S. Liu, and Harry L. Swinney, “Flow Regimes in a Circular Couette System with Independently Rotating Cylinders,” Journal of Fluid Mechanics 164 (1986), pp. 155–83.
DAVID RUELLE SOMETIMES SAID Ruelle. 132.
“ALWAYS NONSPECIALISTS FIND” Ruelle.
HE WROTE A PAPER “On the Nature of Turbulence.”
OPINIONS STILL VARIED They quickly discovered that some of their ideas had already appeared in the Russian literature; “on the other hand, the mathematical interpretation which we give of turbulence seems to remain our own responsibility!” they wrote. “Note Concerning Our Paper ‘On the Nature of Turbulence,’” Communications in Mathematical Physics 23 (1971), pp. 343–44.
PSYCHOANALYTICALLY “SUGGESTIVE” Ruelle.
“DID YOU EVER ASK GOD” “Strange Attractors,” p. 131.
“TAKENS HAPPENED” Ruelle.
“SOME MATHEMATICIANS IN CALIFORNIA” Ralph H. Abraham and Christopher D. Shaw, Dynamics: The Geometry of Behavior (Santa Cruz: Aerial: 1984).
“IT ALWAYS BOTHERS ME” Richard P. Feynman, The Character of Physical Law (Cambridge, Mass.: The M.I.T. Press, 1967), p. 57.
DAVID RUELLE SUSPECTED Ruelle.
THE REACTION OF THE SCIENTIFIC PUBLIC “Turbulent Dynamical Systems,” p. 275.
EDWARD LORENZ HAD ATTACHED “Deterministic Nonperiodic Flow,” p. 137.
“IT IS DIFFICULT TO RECONCILE Ibid., p. 140.
HE WENT TO VISIT LORENZ Ruelle.
“DON’T FORM A SELFISH CONCEPT Ueda reviews his early discoveries from the point of view of electrical circuits in “Random Phenomena Resulting from Nonlinearity in the System Described by Duffing’s Equation,” in International Journal of Non-Linear Mechanics 20 (1985), pp. 481–91, and gives a personal account of his motivation and the cool response of his colleagues in a postscript. Also, Stewart, private communication.
“A SAUSAGE IN A SAUSAGE” Rössler.
THE MOST ILLUMINATING STRANGE ATTRACTOR Hénon; he reported his invention in “A Two-Dimensional Mapping with a Strange Attractor,” in Communications in Mathematical Physics 50 (1976), pp. 69–77, and Michel Hénon and Yves Pomeau, “Two Strange Attractors with a Simple Structure,” in Turbulence and the Navier-Stokes Equations, ed. R. Teman (New York: Springer-Verlag, 1977).
IS THE SOLAR SYSTEM Wisdom.
“TO HAVE MORE FREEDOM” Michel Hénon and Carl Heiles, “The Applicability of the Third Integral of Motion: Some Numerical Experiments,” Astronomical Journal 69 (1964), p. 73.
AT THE OBSERVATORY Hénon.
“I, TOO, WAS CONVINCED” Hénon.
“HERE COMES THE SURPRISE” “The Applicability,” p. 76.
“BUT THE MATHEMATICAL APPROACH” Ibid., p. 79.
A VISITING PHYSICIST Yves Pomeau.
“SOMETIMES ASTRONOMERS ARE FEARFUL” Hénon.
OTHERS ASSEMBLED MILLIONS Ramsey.
“I HAVE NOT SPOKEN” “Strange Attractors,” p. 137.
UNIVERSALITY
“YOU CAN FOCUS” Feigenbaum. Feigenbaum’s crucial papers on universality are “Quantitative Unversality for a Class of Nonlinear Transformations,” Journal of Statistical Physics 19 (1978), pp. 25–52, and “The Universal Metric Properties of Nonlinear Transformations,” Journal of Statistical Physics 21 (1979), pp. 669–706; a somewhat more accessible presentation, though still requiring some mathematics, is his review article, “Universal Behavior in Nonlinear