Chaotic Dynamics: Theory and Practice

Front Matter....Pages i-xii
Complexity and Unpredictable Scaling of Hierarchical Structures....Pages 1-19
Asymptotic State Estimation Using Observers in Dynamical and Control Systems....Pages 21-31
Learning Optimal Representations....Pages 33-41
Multifractal Coding Measures in Dynamics....Pages 43-47
Determination of Fractal Dimensions and Generalized Entropies for Strange Attractors....Pages 49-52
On the Quaternionic Julia Sets....Pages 53-58
Perturbation Theory and Analyticity of Normalizing Transformations for Area Preserving Maps....Pages 59-70
Note on a Complex Eckhaus Equation....Pages 71-73
Integrability of Discrete-Time Systems....Pages 75-90
From Weak to Full Painlevé Property via time Singularities Transformations....Pages 91-99
The Role of Negative Resonances in the Painlevé Test....Pages 101-114
On the Convergence of Series Solutions of Nonintegrable Systems with Algebraic Singularities....Pages 115-128
Phase Transitions within the Fully Developed Chaotic Regime....Pages 129-138
From Dynamical Systems to Local Diffusion Processes....Pages 139-144
Nonintegrability, Separatrices Crossing and Homoclinic Orbits in the Problem of Rotational Motion of a Satellite....Pages 145-159
Relativistic Chaos in Robertson-Walker Cosmologies: The Topological Structure of Space-Time and the Microscopic Dynamics....Pages 161-175
Feedback Control of Chaotic Systems....Pages 177-193
The Structure of Basin Boundaries in a Simple Adaptive Control System....Pages 195-210
A Method For Adaptive Control and Learning in Chaotic Systems....Pages 211-219
Global Bifurcations, Nonlinear and Chaotic Spatio-Temporal Dynamics in Semiconductor Heterostructures....Pages 221-231
Numerical Study of Bifurcations in the BCS Gap Equation....Pages 233-242
Dynamics of Fibre Laser with Nonlinear External Cavity....Pages 243-251
Symbolic Description of Irregular Behaviour in a Laser Model....Pages 253-261
Chaotic Dynamics in Practice: An Electronic Circuit for a Nonlinear Oscillator with Damping, Forcing, and Possible Escape to Infinity....Pages 263-273
Dynamic Analysis of Encephalic Activity....Pages 275-281
Chaotic Response of a Periodically Forced System of Two Competing Microbial Species....Pages 283-295
Irregular Bursting in Model Neurones....Pages 297-300
Spectroscopy and Dynamics of Vibrationally Excited Molecules: A Phase Space Structure Analysis....Pages 301-316
Inhibition of Chaotic Behaviour in Coupled Models of Atmospheric Dynamics and Climate Evolution....Pages 317-326
Evidence for Chaotic Dynamics in the Outer Solar Plasma and the Earth Magnetosphere....Pages 327-339
Time Series Analysis of Magnetospheric Activity Using Nonlinear Dynamical Methods....Pages 341-347
Spectral Properties of Trajectories in Near Integrable Hamiltonian Systems....Pages 349-355
Symmetry Breaking in the Period Doubling Route to Chaos....Pages 357-369
Dissipative Deterministic Chaotic Dynamics Between the Lyapounov Time and the Long Time Limit: A Probabilistic Description....Pages 371-378
Resonant Normal Forms and Applications to Beam Dynamics....Pages 379-388
Analysis of Singularities of the Standard Map Conjugation Function....Pages 389-394
Pade Approximants Applied to the Analysis of the Singularity Structure for Conjugacy Problem....Pages 395-399
Back Matter....Pages 401-418