PEP 630 Nonlinear Dynamics for Physicists

Definition of dynamical systems; phase space and equilibrium states and their classification; nonlinear oscillator with and without dissipation; Van der Pol generator; Poincare map; slow and fast motion; forced nonlinear oscillator: linear and nonlinear resonances; forced generators: synchronization; Poincaré indices and bifurcations; solitons; shock waves; weak turbulence; regular patterns in dissipative media; and chaos: fractal dimension, and Lyapunov exponents. Typical textbooks: H.D.I. Abarbanel, M.I. Rabinovich, and M.M. Sushchik, Introduction to Nonlinear Dynamics for Physicists; R.H. Abraham and C.D. Shaw, Dynamics: The Geometry of Behavior.




Department of Physics