Chaotic Dynamics, Softcover reprint of the original 1st ed. 1992 Theory and Practice NATO Science Series B: Series, Vol. 298

Many conferences, meetings, workshops, summer schools and symposia on nonlinear dynamical systems are being organized these days, dealing with a great variety of topics and themes -classical and quantum, theoretical and experimental. Some focus on integrability, or discuss the mathematical foundations of chaos. Others explore the beauty of fractals, or examine endless possibilities of applications to problems of physics, chemistry, biology and other sciences. A new scientific discipline has thus emerged, with its own distinct philosophical viewpoint and an impressive arsenal of new methods and techniques, which may be called Chaotic Dynamics. Perhaps its most outstanding achievement so far has been to shed new light on many long­ standing issues involving complicated, irregular or "chaotic" nonlinear phenomena. The concepts of randomness, complexity and unpredictability have been critically re-examined and the fundamental importance of scaling, self-similarity and sensitive dependence on parameters and initial conditions has been firmly established. In this NATO ASI, held at the seaside Greek city of Patras, between July 11- 20, 1991, a serious effort was made to bring together scientists representing many of the different aspects of Chaotic Dynamics. Our main aim was to review recent advances, evaluate the current state of the art and identify some of the more promising directions for research in Chaotic Dynamics.

Complexity and Unpredictable Scaling of Hierarchical Structures.- Asymptotic State Estimation Using Observers in Dynamical and Control Systems.- Learning Optimal Representations.- Multifractal Coding Measures in Dynamics.- Determination of Fractal Dimensions and Generalized Entropies of Strange Atractors.- On the Quaternionic Julia Sets.- Perturbation Theory and Analyticity of Normalizing Transformations for Area Preserving Maps.- Note on a Complex Eckhaus Equation.- Integrability of Discrete-Time Systems.- Prom Weak to Full Painlevé Property Via Time Singularities Transformations.- The Role of Negative Resonances in the Painlevé Test.- On the Convergence of Series Solutions of Nonintegrable Systems With Algebraic Singularities.- Chaotic Phase Transitions Within the Fully Developed Regime.- From Dynamical Systems to Local Diffusion Processes.- Nonintegrability, Separatrices Crossing and Homoclinic Orbits in the Problem of Rotational Motion of a Satellite.- Relativistic Chaos in Robert son-Walker Cosmologies: The Topological Structure of Space-Time and Microscopic Dynamics.- Feedback Control of Chaotic Systems.- The Structure of Basin Boundaries in a Simple Adaptive Control System.- A Method for Adaptive Control and Learning in Chaotic Systems.- Global Bifurcations, Nonlinear and Chaotic Spatio-Temporal Dynamics in Semiconductor Heterostructures.- Numerical Study of Bifurcations in the BCS Gap Equation.- Dynamics of Fibre Laser With Nonlinear External Cavity.- Symbolic Description of Irregular Behaviour in a Laser Model.- Chaotic Dynamics in Practice: An Electronic Circuit for a Nonlinear Oscillator With Damping, Forcing and Possible Escape to infinity.- Dynamic Analysis of Encephalic Activity.- Chaotic Response of a Periodically Forced System of Two CompetingMicrobial Species.- Irregular Bursting in Model Neurones.- Spectroscopy and Dynamics of Vibrationally Excited Molecules: A Phase Space Structure Analysis.- Inhibition of Chaotic Behaviour in Coupled Models of Atmospheric Dynamics and Climate Evolution.- Evidence for Chaotic Dynamics in the Outer Solar Plasma and the Earth Magnetosphere.- Time Series Analysis of Magnetospheric Activity Using Nonlinear Dynamical Methods.- Spectral Properties of Trajectories in Near Integrable Hamiltonian Systems.- Symmetry Breaking in the Period-Doubling Route to Chaos.- Dissipative Deterministic Chaotic Dynamics Between the Lyapounov Time and Long Time Limit: A Probabilistic Description.- Resonant Normal Forms and Applications to Beam Dynamics.- Analysis of Singularities of the Standard Map Conjugation function.- Padé Approximants Applied to the Analysis of the Singularity Structure for Conjugacy Problem.- Contributors.