turkmath.org

The origins of the subject of dynamical systems lie in classical mechanics, in the study of such fundamental problems as the stability of the solar system.  A theme that traces back to Noether's theorem is that symmetries in such physical systems must occur for a reason: for example, if the motion of a system does not depend on position in space, then there must be a conserved quantity, such as angular momentum.   I will discuss, in the broader contexts of modern dynamics, how this theme expands and reoccurs in beautiful ways: on the one hand, a typical object has the minimum amount of symmetry possible, and on the other hand, a little extra symmetry implies a lot of symmetry, a phenomenon known as rigidity.