MA 277: Nonlinear Dynamical Systems and Chaos
Credits: 3:0
Conservative Systems: Hamiltonians, canonical transformations, nonlinear pendulum, perturbative methods, standard map, Lyapunov exponents, chaos, KAM theorem, Chirikov criterion.
Dissipative Systems: logistics map, period doubling, chaos, strange attractors, fractal dimensions, Smale horseshoe, coupled maps, synchronization, control of chaos.
Suggested books and references:
- Lichtenberg, A. J. and Lieberman, M. A., Regular and Stochastic motion, Springer-Verlag, 1983.
- Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems and bifurcations of vector fields, Springer-Verlag, 1983.