EVENT DETAILS AND ABSTRACT

Title: Mandelpinski Necklaces in the Parameter Plane for Singularly Perturbed Rational Maps
Speaker: Bob Devaney
Speaker Info: Boston University
Brief Description:
Special Note:
Abstract:

In this lecture we consider rational maps of the form z^n + C/z^n where n > 2. When C is small, the Julia sets for these maps are Cantor sets of circles and the corresponding region in the C-plane (the parameter plane) is the McMullen domain. We shall show that the McMullen domain is surrounded by infinitely many disjoint simple closed curves called Mandelpinski necklaces. The k^th necklace contains exactly (n-2)n^k + 1 parameters that are the centers of baby Mandelbrot sets and the same number of parameters that are centers of Sierpinski holes, i.e., disks in the parameter plane for which the corresponding Julia sets are Sierpinski curves (sets that are homeomorphic to the Sierpinski carpet fractal). We shall also briefly describe other interesting structures in the parameter plane.