Complex Analysis, Dynamics and Geometry Seminar

We study the parameter space ${\mathcal S}_p$ for cubic polynomials with a marked critical point of period $p$. We will show that for every escape region ${\mathcal E}\subset {\mathcal S}_p$, and every rational parameter angle $\phi$, the parameter ray ${\mathfrak R}_{\mathcal E}(\phi)$ lands at some uniquely defined point in the boundary of the escape region $\partial{\mathcal E}$. This point is necessarily either critically finite or parabolic. Joint work with John Milnor. Speaker(s): Araceli Bonifant (URI)