Chaos and Statistical Methods

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.