Introduction to Iteration Theory

On behalf of the Department of Mathematics and Statistics, you are cordially invited on a seminar to be conducted by Dr. Ziyad Al-Sharawi, Associate Professor, AUS Department of Mathematics and Statistics.

Abstract

Consider the quadratic function y = f(x) = ax(1 - x) for 0 < a < 4: It is obvious to all high school students that we have a parabola, which concaves downward with x-intercepts at x = 0, 1 and with a critical point in between. But, what happens if we iterate the function? Suppose we start with an x-value b in the interval [0, 1]; and we start iterating the function, i.e., we obtain the sequence: b, f(b), f(f(b)), f(f(f(b)))), and so on.... Does this sequence converge? In general, what happens to this sequence? In this talk, we focus on this simple quadratic map and use it to introduce the audience to the Field of Iteration Theory. Iteration Theory is in fact studying the dynamics of first order difference equations. This subject is very interesting and rich with notions like the period doubling phenomenon and chaos.

For more information, please contact [email protected].