## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Exploring the parameter space of an IFS

**Speaker:** Sarah Koch

**Speaker Info:** University of Michigan

**Brief Description:**

**Special Note**:

**Abstract:**

In 1985, M. Barnsley and A. Harrington studied the iterated function system f_c,g_c: C to C given by {f_c:z maps to cz+1, g_c:z maps to cz-1}, where c in D-{0}. For a given value of the parameter c, there is a nonempty attractor in the dynamical plane. A natural subset to consider in parameter space is the corresponding connectedness locus, which we (suggestively) denote as M; it has been studied by several mathematicians, including T. Bousch, who proved that it is both connected, and locally connected. In 2002, C. Bandt proved that the complement of M has at least two connected components; that is, M is NOT full as a subset of D-{0}. In this talk, we explore more of the topology of M. We compare/contrast the discussion of this parameter space to the study of the parameter space for quadratic polynomials p_c:z maps to z^2+c.
This is joint work with D. Calegari and A. Walker.

**Date:** Tuesday, November 11, 2014

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Bryna Kra

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

**Contact Phone:** 847-491-5567

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