Chaos and Statistical Methods

Inhaltsverzeichnis

• I General Concepts.
• Coarse Graining Revisited —The Case of Macroscopic Chaos.
• Gibbs Variational Principle and Fredholm Theory for One-Dimensional Maps.
• Truncated Development of Chaotic Attractors in a Map when the Jacobian is not Small.
• II Fractals in Dynamical and Stochastic Systems.
• On the Dynamics of Iterated Maps VIII: The Map z??(z+1/z), from Linear to Planar Chaos, and the Measurement of Chaos.
• Self-Similar Natural Boundaries of Non-Integrable Dynamical Systems in the Complex t Plane.
• Topological Phase Transitions.
• Dynamical System Related to an Almost Periodic Schrödinger Equation.
• Mean Field Hausdorff Dimensions of Diffusion-Limited and Related Aggregates.
• III Onset of Chaos.
• Stability of the Scenarios Towards Chaos.
• Functional Renormalization-Group Equations Approach to the Transition to Chaos.
• Collapse of Tori in Dissipative Mappings.
• Periodic Forcing Near Intermittency Threshold — Resonance and Collapse of Tori.
• Perturbation Theory Analysis of Bifurcations in a Three-Dimensional Differential System.
• IV One-Dimensional Mappings.
• Noise-Induced Order — Complexity Theoretical Digression.
• Symbolic Dynamics Approach to Intermittent Chaos — Towards the Comprehension of Large Scale Self-Similarity and Asymptotic Non-Stationarity.
• Diffusion and Generation of Non-Gaussianity in Chaotic Discrete Dynamics.
• Analytic Study of Power Spectra of Intermittent Chaos.
• V Bifurcations and Normal Forms.
• Versal Deformation of Singularities and Its Applications to Strange Attractors.
• Some Codimension-Two Bifurcations for Maps, Leading to Chaos.
• Bifurcations in Doubly Diffusive Convection.
• Strange Attractors in a System Described by Nonlinear Differential-Difference Equation.
• Coupled Chaos.
• Bifurcations in 2D Area-Preserving Mappings.
• VI SolitonSystems.
• Chaotic Behavior Induced by Spatially Inhomogeneous Structures such as Solitons.
• Chaotic Behaviour of Quasi Solitons in a Nonlinear Dispersive System.
• VII Fluid Dynamics.
• Inviscid Singularity and Relative Diffusion in Intermittent Turbulence.
• Computational Synergetics and Innovation in Wave and Vortex Dynamics.
• A Scalar Model of MHD Turbulence.
• The Analytic Structure of Turbulent Flows.
• Low Prandtl Number Fluids, a Paradigm for Dynamical System Studies.
• Chaotic Attractors in Rayleigh-Benard Systems.
• Onset of Chaos in Some Hydrodynamic Model Systems of Equations.
• VIII Chemical and Optical Systems.
• Instabilities and Chaos in a Chemical Reaction.
• Optical Turbulence.
• IX Anomalous Fluctuations.
• Scaling Theory of Relative Diffusion in Chaos and Turbulence.
• 1/f Resistance Fluctuations.
• Index of Contributors.