Complex dynamics and zeros of derivatives

Faculty Member

Aimo Hinkkanen

Project Image

This is a continuation of the IGL project of the same name from Fall 2016. The team will produce graphics of Julia sets of suitable rational functions (these are fractals arising in complex dynamics) to illustrate the behavior of the zeros of the derivatives of a given function. The zeros of the first derivative of a function are poles of the associated Newton's method function, and the zeros of the second derivative of a function are among the zeros of the derivative of the Newton's method function, which, in turn, are often connected to certain components of the Fatou set (the complement of the Julia set) of the Newton's method function. For this reason, complex dynamics has been used to study the location of the zeros of the derivatives of a given function. Graphics will be produced to illustrate situations that can occur.

Team Meetings

Weekly

Project Difficulty

Beginner

Undergrad Prerequisites

Completion of Calculus 3