Abstract
Turbulence was one of the key phenomena that motivated the resurgence of interest in nonlinear dynamical systems. It was, after all, investigations into the mechanisms for turbulence that led Ruelle and Takens to invent the term “strange attractor” in 1971. The turbulence that is described by strange attractors is “turbulence in time” (Schuster, 1988) -- deterministic chaos, or temporal chaos in current terminology. In the past decade, a vocabulary for the quantitative characterization of temporal chaos has been developed, and has been used to describe and analyze an incredible variety of phenomena in practically all fields of science and engineering. The dimensions of strange attractors, and the entropies and Lyapunov exponents describing motions on them, have been used to analyze heartbeats and brain waves, chemical reactions, lasers, the economy, x-ray emissions of stars, flames, and fluid flow ...
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