## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**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

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Yair Hartman

**Contact email:** hartman@math.northwestern.edu

**Contact Phone:** 224-427-0898

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