Department of Physics

10ΕΛΕ06 Non-Linear Dynamical Systems

Course webpage:  https://eclass.uoa.gr/courses/PHYS289

Course outline

Course content

• Dynamical systems as continuous flows in phase space and as maps. Equilibrium points and stability. Bifurcations in one-dimensional systems.
• Two-dimensional dynamical systems. Linear dynamics in two dimensions.
  Poincaré-Bendixson theorem. Limit cycles. Hopf bifurcation. Stability of limit cycles. Parametric instability.
• Non-linear oscillations. Perturbation methods. Method of multiple time scales.
• Introduction to chaotic dynamics. Lorenz system. Lyapunov exponents.
• Quasi-linear 1^st order partial differential equations. Characteristics and formation of shock waves and applications. Burgers equation.
• Non-linear waves. Boussinesq equations. Korteweg-de Vries and non-linear Schrödinger equations. Introduction to soliton theory.