Complex Analysis, Dynamics and Geometry Seminar

The Yoccoz inequality provides a bound on the size of the limbs of the Mandelbrot set, however this bound is not sharp in most cases. Near parabolic parameters, for example the cusp of the main cardiod, the bound coming from the Yoccoz inequality appears to be far from optimal. Parabolic implosion, the theory of perturbations of parabolic functions, provides tools to understand the geometry of the Mandelbrot set near parabolic parameters. In this talk I will discuss the possibility of using parabolic implosion to improve the Yoccoz inequality near parabolic parameters. Speaker(s): Alex Kapiamba (U(M))