MATH 3DC3, Fall 2018
DISCRETE DYNAMICAL SYSTEMS AND CHAOS
Learn the basic rigorous mathematical ideas behind the Julia and Mandelbrot sets. Learn what a fractal is, how to generate fractals like the Beardsley fern or the Koch snowflake, and how fractal dimension is defined. Iterate using Newton's method to obtain beautiful pictures. Find out what is meant by chaos and explore chaotic dynamical systems. Play the chaos game. Learn what nonlinear models can predict about the world we live in. In the course you will learn tools, both analytical and computational to explore discrete dynamical systems. You will learn how to iterate maps algebraically and graphically, how to detect fixed points and periodic points, and how to determine their stability. You will learn about bifurcation diagrams and orbit diagrams. You will learn why "period 3" implies chaos and the significance of the Sarkovskii ordering. You will be introduced to computer software, and will be expected to use this software to explore the dynamics generated by iterating nonlinear maps. However, no prior experience with computer programming is necessary, just some curiosity and a willingness to learn.
INSTRUCTOR: S. Alama
Iteration of functions: orbits, graphical analysis, fixed and periodic points, stability, bifurcations, chaos, fractals, Julia sets.
Three lectures; one term
Prerequisite(s): One of MATH 2A03, 2X03, 2ZZ3, or ISCI 2A18 A/B
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS