| Introduction | |
| Chaos before Chaos | |
| Frequency Demultiplication | p. 4 |
| On Nonlinear Differential Equations of the Second Order: I. The Equation [actual symbol not reproducible] - k(1 - y[superscript 2]) y + y = b[lambda]kcos([lambda]t + a), k Large | p. 6 |
| Nonlinear Vibrations of a Buckled Beam under Harmonic Excitation | p. 16 |
| Random Phenomena Resulting from Nonlinearity in the System Described by Duffing's Equation | p. 26 |
| Description and Quantification of Chaotic Behavior | |
| Strange Attractors | p. 40 |
| Geometry from a Time Series | p. 52 |
| Deterministic Representation of Chaos in Classical Dynamics | p. 57 |
| Determining Lyapunov Exponents from a Time Series | p. 61 |
| Analytical Methods | |
| A Partial Differential Equation with Infinitely Many Periodic Orbits: Chaotic Oscillations of a Forced Beam | p. 98 |
| Second Order Averaging and Bifurcations to Subharmonics in Duffing's Equation | p. 129 |
| Subharmonic and Homoclinic Bifurcations in a Parametrically Forced Pendulum | p. 143 |
| Power Spectra of Strange Attractors near Homoclinic Orbits | p. 156 |
| The Mel'nikov's Technique for Highly Dissipative Systems | p. 160 |
| The Variational Approach to the Theory of Subharmonic Bifurcations | p. 172 |
| The Refined Approximate Criterion for Chaos in a Two-State Mechanical Oscillator | p. 198 |
| Analytical Condition for Chaotic Behaviour of the Duffing Oscillator | p. 211 |
| Classical Nonlinear Oscillators: Duffing, Van der Pol and Pendulum | |
| Universal Scaling Property in Bifurcation Structure of Duffing's and of Generalized Duffing's Equations | p. 219 |
| Superstructure in the Bifurcation Set of the Duffing's Equation, [actual symbol not reproducible] + dx + x + x[superscript 3] = f cos([omega]t | p. 224 |
| On the Understanding of Chaos in Duffing's Equation Including a Comparison with Experiment | p. 229 |
| Chaotically Transitional Phenomena in the Forced Negative-Resistance Oscillator | p. 234 |
| Period-Doubling Cascades and Devil's Staircases of the Driven Van der Pol Oscillator | p. 242 |
| Chaotic States and Routes to Chaos in the Forced Pendulum | p. 249 |
| Josephson Junctions and Circle Maps | p. 263 |
| Resonance and Symmetry Breaking for the Pendulum | p. 267 |
| Other Oscillatory Systems | |
| Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors | p. 289 |
| Chaos after Period-Doubling Bifurcations in the Resonance of an Impact Oscillator | p. 296 |
| Devil's Attractors and Chaos of a Driven Impact Oscillator | p. 300 |
| A Periodically Forced Piecewise Linear Oscillator | p. 304 |
| Complex Dynamics of Compliant Off-Shore Structures | p. 331 |
| Chaos Generated by the Cutting Process | p. 352 |
| The Stability of Modes at Rest in a Chaotic System | p. 355 |
| Chaotic Motion of an Elastic-Plastic Beam | p. 366 |
| Chua's Circuit Family | p. 371 |
| Chaos via Torus Breakdown | p. 382 |
| Chaos in Noisy Systems | |
| Fluctuations and the Onset of Chaos | p. 401 |
| Noise versus Chaos in Acousto-optic Bistability | p. 405 |
| Generalized Multistability and Noise-Induced Jumps in a Nonlinear Dynamical System | p. 412 |
| Chaotic Distribution of Non-Linear Systems Perturbed by Random Noise | p. 419 |
| Influence of Perturbations on Period-Doubling Bifurcation | p. 423 |
| Chaos In a Noisy Mechanical System with Stress Relaxation | p. 428 |
| Homoclinic Chaos in Systems Perturbed by Weak Langevin Noise | p. 434 |
| Strange Nonchaotic Attractors | |
| Quasiperiodically Forced Dynamical Systems with Strange Nonchaotic Attractors | p. 452 |
| Dimensions of Strange Nonchaotic Attractors | p. 470 |
| Route to Chaos via Strange Non-chaotic Attractors | p. 476 |
| Spatial Chaos | |
| Chaos as a Limit in a Boundary Value Problem | p. 484 |
| On the Connection between Statical and Dynamical Chaos | p. 488 |
| Spatially Complex Equilibria of Buckled Rods | p. 494 |
| Spatial Chaos and Localization Phenomena in Nonlinear Elasticity | p. 524 |
| Soliton Chaos Models for Mechanical and Biological Elastic Chains | p. 530 |
| Spatiotemporal Dynamics in a Dispersively Coupled Chain of Nonlinear Oscillators | p. 537 |
| Fractal Basin Boundaries | |
| Fractal Basin Boundaries | p. 548 |
| Fractal Basin Boundaries and Homoclinic Orbit for Periodic Motion in a Two-Well Potential | p. 577 |
| Fractal Basin Boundaries of an impacting Particle | p. 581 |
| Integrity Measures Quantifying the Erosion of Smooth and Fractal Basins of Attraction | p. 588 |
| References | p. 611 |
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