Although we normally think of classical mechanical systems as being completely predictable, the complexity of real-world systems usually means that we have incomplete information about the initial conditions. Chaotic systems can be characterized as those for which a very small change in the initial conditions will lead to a large change in the evolution of the system. Thus for such systems, incompleteness of information about the initial conditions leads to a loss of predictability of the evolution of the system. Since chaotic behaviour has been observed in many important everyday situations, from the rhythm of the heart to evolution of weather patterns to the orbits of asteroids around the sun, it is clearly important to be able to characterize chaotic systems and extract as much information as possible about their behaviour. This course serves as a first introduction to this fascinating area of modern physics and mathematics.

Lecturer