Complex Analysis, Dynamics and Geometry Seminar

Associated to every polynomial is a compact subset of the complex plane, called the filled Julia set, which is a fundamental object in understanding they dynamics of that polynomial. Douady showed that when a polynomial without parabolic cycles is perturbed, the corresponding filled Julia sets vary continuously. Over the course to two talks we will examine this phenomenon. In the first talk we will give an introductory overview of the continuity of filled Julia sets and parabolic implosion, the obstruction to continuity caused by parabolic cycles.
In the second talk we will discuss the space of compact sets which arise as limits of quadratic polynomials and ongoing efforts to describe its topology. Speaker(s): Alex Kapiamba (U(M))