Title: Finding cycles in discrete dynamical systems.

Abstract: Discrete dynamical systems often exhibit chaotic behavior, and as a result finding cycles can be computationally expensive. I present a new approach to this problem, based on adding a nonlinear feedback that stabilizes the cycles. We are then able to find cycles numerically in polynomial time. The main theoretical new insight is casting the problem in the language of complex analysis, and finding new complex polynomials that generalize work of Ted Suffridge that optimize the number of steps one needs in order to stabilize the system. This is joint work with D. Dmitrishin, A. Khamitova and A. Stokolos.