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Dimensions and Entropies in Chaotic Systems
Proceedings of an International Workshop at the Pecos River Ranch, New Mexico, September 11-16, 1985
1 online resource (ix, 257 pages 139 illustrations)
This volume contains a collection of papers on methods for the quantification of chaotic dynamical systems. New developments in the theory of nonlinar dynamical systems show that irregular behavior can be generated by deterministic systems with very few degrees of freedom. The concepts of fractal dimensions, dynamical entropies and Lyapunov exponents have been introduced in order to estimate the number of degrees of freedom involved in a given signal or time series. This book provides insight into the mathematical problems of dimensional analysis of erratic data, into the problems of its numerical implementation, and also into its practical realization in a series of different experiments. The limits of predictability of chaotic systems and the reliability and accuracy of different methods for computing dimensions are discussed. New experimental results on spatio-temporal chaos, dimensions of clouds, lasers, brain waves, and hydrodynamical and solid state systems are presented.
Introduction -- General Theory, Mathematical Aspects of Dimensions, Basic Problems -- Numerical and Experimental Problems in the Calculation of Dimensions and Entropies -- Computation of Lyapunov Exponents -- Reliability, Accuracy and Data Requirements of Different Algorithms -- Analysing Spatio Temporal Chaos -- Experimental Results and Applications -- Index of Contributors.