Required readings and viewings:
Unit 1:
- The logistic map app
- That video I showed of Hyperion tumbling
Unit 2:
- The logistic map app
- That video I showed that zooms in on the Mandelbrot set.
Units 3-5:
Unit 7-9:
Unit 10:
- A youtube video about spin-lock in the earth-moon system
- A 2013 article from the Boston Globe about Diana Dabby and her latest creation: a web-based chaotic variation generator.
- One Flat Thing, Reproduced
Optional (but useful) things to check out:
Unit 2:
- A gorgeous video of an evolving 3D fractal surface.
- A 'chalkmation' youtube video - complete with music - about the Mandelbrot set (warning: a bit of foul language at the end).
- Google labs' Julia Map website, which uses the Google Maps API (!) to render fractals.
Unit 5-6:
Unit 7:
- Papers about UPOs and attractor structure: P. Cvitanovic, "Invariant measurement of strange sets in terms of circles," Phys Rev Lett 61:2729 (1988) — and a couple of more-technical ones in Nonlinearity in 1990 (vol 3 pp 325-386).
- Papers about finding UPOs: G. Gunaratne et al., ""Chaos beyond Onset: A Comparison of Theory and Experiment," Phys Rev Lett 63:1-4 (1989); P. So et al., "Extracting unstable periodic orbits from chaotic time-series data," Phys Rev E 55:5398 (1997)
Units 7-9:
- The TISEAN time-series analysis toolkit includes lots of good stuff — including Lyapunov exponent and correlation dimension calculators. The TISEAN site has binaries for UNIX & windows, but you can get Mac binaries here. You may need this fortran library to get it to work. Here are some examples of how to run all of this from MATLAB. If you have brew on your machine, you can simply type 'brew install tisean' (without the quotes, of course). Be aware that TISEAN is not a required element of this course and that it can sometimes be hard to install.
Unit 10:
- Troy Shinbrot's review paper on the control of chaos: "Progress in the control of chaos," Advances in Physics 44:73-111 (1995)
- A list of chaotic music clips from Diana Dabby's 2008 Science article (320(5872): 62-63)
Other useful and/or interesting links:
- The movement of an array of pendula with different lengths
- Video recordings of the lectures from Steve Strogatz's introductory course on nonlinear dynamics and chaos and the Google Books link to his textbook
- xkcd's take on chaos
Lecture Slides (zipfiles of pdfs): please be aware that these are not course notes; they are simply the slides (if any) that were used in the lectures.
There is no textbook for this course, nor any compiled course notes. This course draws upon material from different textbooks, journal papers, conference talks that were never published, and our own experience. The lecture videos are your primary resource for that material.
- Unit 1 (593KB)
- Unit 2 (8.7MB)
- Unit 3 (85KB)
- Unit 4 (14MB)
- There were no slides for Unit 5.
- Unit 6 (758KB)
- Unit 7 (7.2MB)
- Unit 8 (1MB)
- Unit 9 (2MB)
- Unit 10 (13.7MB)
Lecture and Solution Videos (zipfiles of mp4s):
- Unit 1 (223MB)
- Unit 2 (522MB)
- Unit 3 (817MB)
- Unit 4 (443 MB)
- Unit 5 (198 MB)
- Unit 6 (298MB)
- Unit 7 (516MB)
- Unit 8 (685MB)
- Unit 9 (951MB)
- Unit 10 (539MB)