Advance Dynamical Systems (I)

This course is devoted to  Floquet 's theory and Liapunov exponents, Liouville 's Theorem and its applications, Standard Symplectic Form, Symplectic and Infinitesimally Symplectic Transformaions in R^{2n}, Hamiltonian Vector Fields, Reversible Systems and Infinitesimally Reversible Linear Maps, Symbolic Dynamics and the Shift Map, Chaos and Strange Attractors, an introduction to Slow-Fast Systems and singular perturbation theory.