Ma 4. Introduction to Mathematical Chaos
MW 13:00 - 14:25
Office: 282 Sloan
Office Hours: by appointment
Teaching Assistant: Vaibhav
Office: 260 Sloan
Office Hours: Tuesday, 3-4 pm
The analysis of how a complex system changes over time is known as dynamics. The interaction between only a few simple equations can produce enormously complex behavior, such as the population of different species within an ecosystem or the orbits of the planets within our solar system. Some complex systems can appear totally random, and are said to be chaotic. Such systems are not only highly unpredictable, but the slightest nudge can set them off on a wildly different course, a feature known as the 'butterfly effect'.
In this course we will study the most interesting examples and the most basic features of dynamical systems:
1 B.Hasselblatt, A.Katok, "A first course in Dynamics",
2 R.Devaney, "An introduction to chaotic dynamical systems",
3 M.Brin, G.Stuck, "Introduction to dynamical systems",
4 B.Hasselblatt, A.Katok, "Introduction to the modern theory of Dynamical Systems".
Additional references will be given for a few topics not covered by these books.
Grading: Weekly homework 50%, midterm exam 20%, final exam 30%.
Collaboration Policy: You may discuss homework problems with other students, but solutions should be written up individually in your own words. Take-home exams must be your own work.
Infinite Fractal Loop
The Mandelbrot and Julia sets
Famous dynamical systems in motion