The aim of this course is to introduce a selection of fundamental topics in Applied Mathematics. Topics include: fixed points, bifurcations, phase portraits, conservative and reversible systems. Index theory, Poincaré-Bendixson theorem, Lienard systems, relaxation oscillators. Hopf bifurcations, quasi periodicity and Poincaré maps, applications to oscillating chemical reactions and Josephson junctions. Chaos on a strange attractor, Lorentz map, logistic map, Hénon map, Lyapunov exponents. Fractals.

*Course content subject to change