Title | Dimensions and Entropies in Chaotic Systems [electronic resource] : Quantification of Complex Behavior / edited by Gottfried Mayer-Kress |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-642-71001-8 |
Descript | IX, 257 p. online resource |
I Introduction -- Introductory Remarks -- II General Theory, Mathematical Aspects of Dimensions, Basic Problems -- The Characterization of Fractal Measures as Interwoven Sets of Singularities: Global Universality at the Transition to Chaos -- Fractal Measures (Their Infinite Moment Sequences and Dimensions) and Multiplicative Chaos: Early Works and Open Problems -- On the Hausdorff Dimension of Graphs and Random Recursive Objects -- Chaos-Chaos Phase Transition and Dimension Fluctuation -- Hausdorff Dimensions for Sets with Broken Scaling Symmetry -- Scaling in Fat Fractals -- III Numerical and Experimental Problems in the Calculation of Dimensions and Entropies -- Lorenz Cross-Sections and Dimension of the Double Rotor Attractor -- On the Fractal Dimension of Filtered Chaotic Signals -- Efficient Algorithms for Computing Fractal Dimensions -- Using Mutual Information to Estimate Metric Entropy -- IV Computation of Lyapunov Exponents -- Intermediate Length Scale Effects in Lyapunov Exponent Estimation -- Comparison of Algorithms for Determining Lyapunov Exponents from Experimental Data -- A Measure of Chaos for Open Flows -- V Reliability, Accuracy and Data-Requirements of Different Algorithms -- An Approach to Error-Estimation in the Application of Dimension Algorithms -- Invisible Errors in Dimension Calculations: Geometric and Systematic Effects -- Methods for Estimating the Intrinsic Dimensionality of High-Dimensional Point Sets -- VI Analysing Spatio Temporal Chaos -- Characterizing Turbulent Channel Flow -- Characterization of Chaotic Instabilities in an Electron-Hole Plasma in Germanium -- Instabilities, Turbulence, and the Physics of Fixed Points -- VII Experimental Results and Applications -- Determination of Attractor Dimension and Entropy for Various Flows: An Experimentalistโs Viewpoint -- Transition from Quasiperiodicity into Chaos in the Periodically Driven Conductivity of BSN Crystals -- Dimension and Entropy for Quasiperiodic and Chaotic Convection -- Experimental Study of the Attractor of a Driven Rayleigh-Bรฉnard System -- Dimension Measurements from Cloud Radiance -- Chaos in Open Flow Systems -- Lasers and Brains: Complex Systems with Low-Dimensional Attractors -- Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle -- Problems Associated with Dimensional Analysis of Electroencephalogram Data -- Index of Contributors