Dynamical Systems: Linear systems, fixed points, stability, bifurcations, limit cycles. Nonlinear oscillators, perturbation theory. 3D dynamics, Lorentz model and an introduction to chaotic dynamics. Lyapunov exponents. Discrete maps. Fractals.

Hamiltonian Chaos: Review of analytical mechanics, Liouville theorem, Hamilton-Jacoby equations, integrability. Canonical perturbation theory, resonances and invariant tori, KAM theorem. Transition to chaos, chaotic dynamics, ergodicity and mixing.Kolmogorov-Sinai entropy, chaotic diffusion.