PMath 370 Chaos and Fractals

Winter 2012

University of Waterloo - Waterloo, Ontario, Canada

This course is designed to introduce a wide range of students to the mathematical foundations of chaos, fractals, and discrete dynamical systems. Many students are intrigued by the scientific, visual, and computing aspects of chaos and fractals, but do not have much idea of the mathematics involved. This mathematics can be introduced to a student who has a background of calculus and linear algebra.

Basic Information

Instructor : Kevin Hare,
Office: MC 5086,
Phone: Ext 35556.
Office Hours : Mondays 10:00-11:30, Wednesday 3:00-4:30
TA Office Hours : Mondays 2:30-3:30 (MC 5050)
Lectures MWF 12:30pm-1:20pm Room MC 4042

Useful links of examples from class

Course Outline

Course Outline
Periodic Points - iterates of functions, fixed points, basins of attraction, periodic points, attracting/repelling points, bifurcations, Sharkovsky order.
Chaos - Transitivity, strong chaos, conjugacy, linear functions, nonlinear maps.
Fractals - Dimensions, Julia sets, Mandelbrot sets, iterated function systems.
Anything else I happen to think is interesting at the time.

Assignments and Sample solutions

Exams

Midterm Exam: February 15th, 12:30-1:20, MC 4061
Final Exam: Thursday April 19th, 12:30-3:00, RCH 307
Old Midterm and Final Exams.

Project

[Julia Set 1] [Lorenz Attractor] [Julia Set 2]

This page was last updated on by K. G. Hare