Q&A

The theory of dynamical systems provides a means for understanding complex behaviour in a broad range of applications. This course is an introduction to the theory, with emphasis on chaotic dynamics. We will study continuous systems (differential equations) and discrete systems (iterated maps). I aim to provide a broad overview of the subject as well as an in-depth analysis of specific examples. The course is intended for students in mathematics, engineering, and science.

The topics include: bifurcations (transcritical, pitchfork, subcritical, supercritical, Hopf), stable and unstable manifolds, dissipative systems, attractors, logistic map, period-doubling, Feigenbaum sequence, renormalization, chaos, Lyapunov exponent, fractals, Cantor set, Hausdorff dimension, Lorenz system, nonlinear oscillations, quasiperiodicity, Hamiltonian systems, integrability, resonance, KAM tori, homoclinic intersections, Melnikov's method.

linear algebra, differential equations

homework assignments, final exam/project