Introduction to Nonlinear Dynamics for Physicists

1. Introduction -- 2. Nonlinear oscillator without dissipation -- 3. Equilibrium states of a nonlinear oscillator with dissipation -- 4. Oscillations in systems with nonlinear dissipation-generators -- 5. The Van der Pol generator -- 6. The Poincaré map -- 7. Slow and fast motions in systems with one degree of freedom -- 8. Forced nonlinear oscillators: linear and nonlinear resonances -- 9. Forced generator: Synchronization -- 10. Competition of modes -- 11. Poincaré indices and bifurcations of equilibrium states -- 12. Resonance interactions between oscillators -- 13. Solitons -- 14. Steady propagation of shock waves -- 15. Formation of shock waves -- 16. Solitons. Shock Waves. Wave Interaction. The spectral approach -- 17. Weak turbulence. Random phase approximation -- 18. Regular patterns in dissipative media -- 19. Deterministic chaos. Qualitative description -- 20. Description of a circuit with chaos. Chaos in maps -- 21. Bifurcations of periodic motions. Period doubling -- 22. Controlled nonlinear oscillator. Intermittency -- 23. Scenarios of the onset of chaos. Chaos through quasi-periodicity -- 24. Characteristics of chaos. Experimental observation of chaos -- 25. Multidimensional chaos. Discrete Ginzburg-Landau model -- 26. Problems to accompany the lectures