Universality in Chaos

This book presents developments in the study of the chaotic behaviour of deterministic systems. It concentrates on the universal aspects of chaotic motions: those qualitative and quantitative predictions which apply to large classes of physical systems. The selection can be divided into roughly four parts. The first part offers a general introduction to deterministic chaos and universality. The second part presents some of the experimental evidence for universality in transitions to turbulence. The third part concentrates on the theoretical investigations of the universality of ideas, and the last part gives a glimpse of the further developments stimulated by the success of the one-dimensional universality theory.

Table of Contents:
Part 1: strange attractors, D.Ruelle; universal behaviour in nonlinear systems, M.J.Feignbaum; simple mathematical models with very complicated dynamics, R.M.May; roads to turbulence in dissapative dynamical systems, J.P.Eckmann. Part 2 Experiments: a Rayleigh Benard experiment - helium in a small box, A.Libchaber and J.Mauer; period doubling cascade in mercury, a quantitative measurement, A.Libchaber et al; onset of turbulence in a rotating fluid, J.P.Gollub and H.L.Swinney; transition to chaotic behaviour via a reproducible sequence of period-doubling bifurcations, M.Giglio et al; intermittency in Rayleigh-Bernard convection, P.Berge et al; representation of a strange attractor from an experimental study of chemical turbulence, J.C.Roux et al; chaos in the Belousov-Zhabotinskii reaction, J.L.Hudson and J.C.Mankin; one-dimensional dynamics in a multicomponent chemical reaction, R.H.Simoyi et al; experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser, F.T.Arrechi et al; evidence for universal chaotic behaviour of a driven nonlinear oscillator, J.Testa et al; phase locking, period boubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells, M.R.Guevara et al. Part 3 Theory: on finite limits sets for transformations on the unit interval, M.Metropolis et al; the universal metric properties of nonlinear transformations, M.J.Feigenbaum; a computer-assisted proof of the Feigenbaum conjectures, O.E.Lanford; the transition to aperiodic behaviour in turbulent systems, M.J.Feigenbaum; universality and the power spectrum at the onset of chaos, M.Nauenberg and J.Rudnick. Part 4 Noise: invariant distributions and stationary correlation functions of one dimensional discrete processes, S.Grossmann and S.Thomae; noise periodicity and reverse bifurcation, E.N.Lorenz; scaling behaviour of chaotic flows, B.A.Huberman and J.Rudnick; universal and power spectra for the reverse bifurcation sequence, A.Wolf and J.Swift; power spectra of strange attractors, B.A.Huberman and A.B.Zisook; spectral broadening of period-doubling bifurcation sequences, J.D.Farmer; fluctuations and the onset of chaos, J.P.Crutchfield and B.A.Huberman; scaling theory for noisy period-doubling transitions to chaos, B.Shraiman et al; scaling for external noise at the onset of chaos. Part 5 Intermittency. Part 6 Period-doubling in higher dimensions. Part 7 Beyond the one-dimensional theory. Part 8 Recent developments. (Part contents)