| Preface | p. v |
| List of Equations | p. xi |
| Pendulum Equations | p. 1 |
| Mathematical pendulum | p. 1 |
| Period of oscillations | p. 5 |
| Underdamped pendulum | p. 10 |
| Nonlinear vs linear equation | p. 15 |
| Isomorphic models | p. 16 |
| Brownian motion in a periodic potential | p. 16 |
| Josephson junction | p. 16 |
| Fluxon motion in superconductors | p. 17 |
| Charge density waves | p. 17 |
| Laser gyroscope | p. 18 |
| Synchronization phenomena | p. 18 |
| Parametric resonance in anisotropic systems | p. 18 |
| Phase-locked loop | p. 19 |
| Dynamics of adatom subject to a time-periodic force | p. 19 |
| The Frenkel-Kontorova model (FK) | p. 19 |
| Solitons in optical lattices | p. 20 |
| Other applications | p. 20 |
| General concepts | p. 20 |
| Phase space | p. 21 |
| Poincare sections and strange attractors | p. 21 |
| Lyapunov exponent | p. 22 |
| Correlation function | p. 22 |
| Spectral analysis | p. 22 |
| Period doubling and intermittency | p. 23 |
| Deterministic Chaos | p. 27 |
| Damped, periodically driven pendulum | p. 27 |
| Transition to chaos | p. 27 |
| Two external periodic fields | p. 32 |
| Dependence on driving frequency | p. 34 |
| Role of damping | p. 35 |
| Symmetry and chaos | p. 36 |
| Diffusion in a chaotic pendulum | p. 39 |
| Analytic methods | p. 41 |
| Period-doubling bifurcations | p. 42 |
| Melnikov method | p. 45 |
| Parametric periodic force | p. 48 |
| Pendulum with vertically oscillating suspension point | p. 49 |
| Transition to chaos | p. 49 |
| Melnikov method | p. 51 |
| Parametric periodic non-harmonic force | p. 52 |
| Downward and upward equilibrium configurations | p. 55 |
| Boundary between locked and running solutions | p. 56 |
| Pendulum with horizontally oscillating suspension point | p. 58 |
| Pendulum with both vertical and horizontal oscillations of the suspension point | p. 62 |
| Parametrically driven pendulum | p. 62 |
| Periodic and constant forces | p. 65 |
| Melnikov method | p. 66 |
| Parametric and constant forces | p. 69 |
| Harmonic balance method | p. 70 |
| Heteroclinic and homoclinic trajectories | p. 71 |
| Numerical calculations | p. 72 |
| External and parametric periodic forces | p. 73 |
| Pendulum subject to a Random Force | p. 77 |
| Noise | p. 77 |
| White noise and colored noise | p. 77 |
| Dichotomous noise | p. 78 |
| Langevin and Fokker-Planck equations | p. 79 |
| External random force | p. 81 |
| Constant and random forces | p. 82 |
| External periodic and random forces | p. 85 |
| Two sources of noise | p. 85 |
| Fokker-Planck equation | p. 86 |
| Ratchets | p. 86 |
| Absolute negative mobility | p. 88 |
| Pendulum with multiplicative noise | p. 89 |
| Parametric periodic and random forces | p. 91 |
| Damped pendulum subject to a constant torque, periodic force and noise | p. 92 |
| Overdamped pendulum | p. 93 |
| Additive white noise | p. 94 |
| Additive dichotomous noise | p. 96 |
| Multiplicative dichotomous noise | p. 99 |
| Additive and multiplicative white noise | p. 102 |
| Multiplicative dichotomous noise and additive white noise | p. 109 |
| Correlated additive noise and multiplicative noise | p. 110 |
| Systems with Two Degrees of Freedom | p. 113 |
| Spring pendulum | p. 113 |
| Dynamic equations | p. 114 |
| Chaotic behavior of a spring pendulum | p. 118 |
| Driven spring pendulum | p. 120 |
| Double pendulum | p. 123 |
| Spherical pendulum | p. 126 |
| Conclusions | p. 131 |
| Bibliography | p. 133 |
| Glossary | p. 139 |
| Index | p. 141 |
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