Universality in Chaos, 2nd edition

Introductory articles: Strange attractors. Universal behaviour in nonlinear systems. Simple mathematical models with very complicated dynamics. Experiments: Onset of turbulence in a rotating fluid Transition to chaotic behaviour via a reproducible sequence of period-doubling bifurcations. Representation of a strange attractor fron an experimental study of chemical turbulence. One-dimensional dynamics in a multicomponent chemical reaction. Experimental evidence of subharmonic bifurcations, multistability and turbulence in a Q-switched gas laser. Evidence for universal chaotic behaviour of a driven nonlinear oscillator. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Theory: Qualitative universality in one dimension. Quantitative universality for one-dimensional period-doublings. A computer-assisted proof of the Feigenbaum conjectures. The transition to aperiodic behaviour in turbulent systems. Noise: Deterministic noise. Invariant distributions and stationary correlation functions of one-dimensional discrete processes. Scaling behaviour of chaotic flows. Power spectra of strange attractors. External noise: Fluctuations and the onset of chaos. Scaling for external noise at the onset of chaos. Intermittency: Intermittent transition to turbulence in dissipative dynamical system. Period-doubling in higher dimensions: A two-dimensional mapping with a strange attractor. Period doubling bifurcations for families of maps on R. Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations. Beyond the one-dimensional theory: Scaling behaviour in a map of a circle onto itself: empirical results. Self-generated chaotic behaviour in nonlinear mechanics. Recent developments: Feigenbaum universality and the thermodynamic formalism. Fractal measures and their singularities: the characterization of strange sets. Fixed points of composition operators.