Abstract:

Understanding the topological and combinatorial structure of the quadratic connectednesslocus, the Mandelbrot set M is largely facilitated by the notion of limbs of hyperbolic components. In this talk I will describe how we can define a notion of limbs of the central hyperbolic component of cubic polynomials. Surprisingly it turns out that such limbs have entry points, know as root points from the rest of the cubic connectedness locus quite far from the central hyperbolic component, where they first appear.