Title: Parameter space structures for perturbations of \(z^n\).
Speaker: Daniel Cuzzocreo
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:
For $1/n + 1/d \leq 1$, $F_{n, d, \lambda} = z^n + \lambda/z^d$ give 1-parameter, $n+d$ degree families of rational maps of the Riemann sphere, which arise as singular perturbations of the polynomial $z^n$. Despite the high degree, symmetries cause these maps to have just a single free critical orbit and thus to form a natural 1-dimensional slice of the full space of rational maps of degree $n+d$. Due to certain similarities with polynomial maps, these families give some of the best-understood examples of non-polynomial rational dynamics in arbitrarily high degree. In this talk we give a survey of some recent results about these families, with a focus on characterizing portions of the fine fractal structure in the parameter space.Date: Tuesday, October 13, 2015