Dynamical Systems

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish in a lake is examples of dynamical systems. A dynamical system has a state determined by a collection of real numbers. Small changes in the state of the system correspond to small changes in the numbers. The course describes the theory of dynamical systems in one and two dimensions. The main areas include bifurcation theory, chaos, attractors, limit cycles, non-linear dynamics.