Nonlinear Oscillations and Waves in Dynamical Systems

1 Dynamical systems. Phase space. Stochastic and chaotic systems. The number of degrees of freedom.- 2 Hamiltonian systems close to integrable. Appearance of stochastic motions in Hamiltonian systems.- 3 Attractors and repellers. Reconstruction of attractors from an experimental time series. Quantitative characteristics of attractors.- 4 Natural and forced oscillations and waves. Self-oscillations and auto-waves.- 5 Conservative systems.- 6 Non-conservative Hamiltonian systems and dissipative systems.- 7 Natural oscillations of non-linear oscillators.- 8 Natural oscillations in systems of coupled oscillators.- 9 Natural waves in bounded and unbounded continuous media. Solitons.- 10 Oscillations of a non-linear oscillator excited by an external force.- 11 Oscillations of coupled non-linear oscillators excited by an external periodic force.- 12 Parametric oscillations.- 13 Waves in semibounded media excited by perturbations applied to their boundaries.- 14 Forced oscillations and waves in active non-self-oscillatory systems. Turbulence. Burst instability. Excitation of waves with negative energy.- 15 Mechanisms of excitation and amplitude limitation of self-oscillations and auto-waves. Classification of self-oscillatory systems.- 16 Examples of self-oscillatory systems with lumped parameters. I.- 17 Examples of self-oscillatory systems with lumped parameters. II.- 18 Examples of self-oscillatory systems with high frequency power sources.- 19 Examples of self-oscillatory systems with time delay.- 20 Examples of continuous self-oscillatory systems with lumped active elements.- 21 Examples of self-oscillatory systems with distributed active elements.- 22 Periodic actions on self-oscillatory systems. Synchronization and chaotization of self-oscillations.- 23 Interaction between self-oscillatory systems.- 24 Examples of auto-waves and dissipative structures.- 25 Convective structures and self-oscillations in fluid. The onset of turbulence.- 26 Hydrodynamic and acoustic waves in subsonic jet and separated flows.- Appendix A Approximate methods for solving linear differential equations with slowly varying parameters.- A.1 JWKB Method.- A.2 Asymptotic method.- A.3 The Liouville—Green transformation.- A.4 The Langer transformation.- Appendix B The Whitham method and the stability of periodic running waves for the Klein—Gordon equation.