February 1
John Vano
University of Texas
Abstract Title: "The Stability of Slinkies, Slide Guitars and the Solar System"
  The KAM theorem (named after A. N. Kolmogorov, V. I. Arnold, and J. K. Moser) establishes a stability theory for perturbations of several interesting classes of dynamical systems, the most famous being the stability of the solar system. In this talk I will describe how I have used this theory to study a model for a laser oscillating in an optically active media. This same model describes other phenomena such as compression waves in elastic media (a slinky) or the transverse displacement of a guitar or violin string. The consequences of our results provide an understanding of the long term behavior of these systems in terms of energy and can also be viewed as answering an infinite dimensional control problem. The talk will be accessible to a wide audience and will include bits of history, interactive props and animations illustrating the various models.