Welcome to M638 Dynamical Systems. The seminal work by Lorenz in 1963, gave scientists insight to recognize a new type of motion called Chaos. Chaotic systems, which can be very simple, are capable of generating erratic behavior that is different from the one produced by quasi-periodic systems with a large number of frequencies of oscillations. Such systems are the subject of this course.

Throughout the semester we will learn different analytic and geometric techniques for studying time-continuous nonlinear dynamical systems. Specific examples from interdisciplinary areas will be covered as time allows it. Mathematical software such as MATLAB will be used to enhance basic concepts. The course is intended for senior undergraduate and first year graduate students in Applied Mathematics, Computational Science, Engineering, Physics, Chemistry, Biology, etc.