Holly Krieger : Bounding recurrence of the critical orbit on the boundary of the Mandelbrot set

Posted by Holly Krieger , part of the Graduate Student Colloquium.

At

Sept. 17, 2012, 4:15 p.m.

In

SEO 636

Abstract

We will discuss the hyperbolic components of the Mandelbrot set, and bound the recurrence of the critical orbit for parameters which are not too close to centers of hyperbolic components. If time permits, we will discuss the application of these bounds to a primitive prime divisors problem in arithmetic dynamics. This is Part 2 of the talk begun by Paul Reschke on September 10. This talk is intended to be accessible to graduate students of all levels; no technical knowledge of complex analysis or complex dynamics is expected.