Title: Entropy for smooth systems
Speaker: Todd Fisher, Brigham Young University
Abstract: Dynamical systems studies the long-term behavior of systems that evolve in time. It is well known that given an initial state the future behavior of a system is unpredictable, even impossible to describe in many cases. The entropy of a system is a number that quantifies the complexity of the system. In studying entropy, the nicest classes of smooth systems are ones that are structurally stable. Structurally stable systems, for example automorphisms of the torus, are those that do not undergo bifurcations for small perturbations. In this case, the entropy remains constant under perturbation. Outside of the class of structurally stable systems, a perturbation of the original system may undergo bifurcation. However, this is a local phenomenon, and it is unclear when and how the local changes in the system lead to global changes in the complexity of the system. We will state recent results describing how the entropy (complexity) of the system may change under perturbation for systems that are not structurally stable.