Project topic ideas
The project is your chance to explore an area that interests you and
to be creative. Computer programs and investigations, artwork,
research papers, physical models...you can do almost anything. However, any
project must have a minimal write-up of around 5 pages. Of course, any
project must relate directly to dynamical systems somehow.
I would like a brief proposal for your project by October 13th; include this in your homework.
The recommended reading is a good place to look for ideas. Feel free
to come to my office hours to discuss ideas. Also, hereare some possible topics to think about:
- The Lorenz equations
- Rossler system
- Complex dynamics (Newton's method, exotic iterated functions...)
- Cellular automata
- Dynamics of card-shuffling.
- Symbolic dynamics
- Julia/Mandelbrot sets
- Fixed-point theorems
- The n-body problem
- Lyapunov exponents and quantitative stability
- Lasers - see the text by Strogatz
- Billiard problems
- Bifurcations and cascades, the Metropolis-Stein-Stein sequence for the logistic map.
- Structural stability theorems