CSCI 4446/5446 Course materials for Spring 2010:

General information and administrivia
 Problem Set 1 : logistic map. You
can use this
app to check that your solutions are correct. Also, you may wish
to take some time this week to review section 1 of the ODE notes
listed below if your knowledge of differential equations is at all
rusty.
 Problem Set 2 : bifurcation diagrams
and Feigenbaum's constant. Again, you can
use
this app to check your solutions. Here are a couple of tutorials
on the unix plotting tool gnuplot
from Duke
and
and UCSC.
 Problem Set 3 : fractals. Here are
some examples of fractals in the wild (click
here and
here) and in various
computational/mathematical systems.
 Problem Set 4 : RungeKutta and the
driven pendulum equations.

Final Project Guidelines . You can
find tech reports that compile projects from some previous semesters
(2010, 2011, 2012, and 2015) here. Search for the
title "Projects in Chaotic Dynamics..."

Problem Set 5 : adaptive RungeKutta and
the Lorenz and Rossler systems.
The following materials may be useful to you as
you do this problem set:
 Problem Set 6 : Poincare sections.
The netnews posts about numerical dynamics that are listed above (PS5)
may be useful here as well.
 Final Project Details
 Problem Set 7 : variational equation.
See the notes listed below.

Problem Set 8 : embedding.
The following materials may be useful to you as
you do this problem set:
 A detailed list of the assigned
reading for PS810 ("Reading assignments for timeseries
analysis")
 Instructions on getting the data for
this problem set and an example of
how to embed a data set .
 Jay Kominek's mpeg movie of
what happens as you change tau in embeddings of data from the Lorenz
system.
 If you want to use TISEAN in the CSEL, this
information about how to access the CSEL machines
may be useful. The machines are called the "elras"
(elra01.cs.colorado.edu et al.). Instructions for downloading and
installing your virtual machine
are here. After
that, run 'sudo aptget install tisean' and then type 'tisean' to
install the TISEAN tools. If you have path problems (can't run it
from where you want to), here's a set of commands that 'user' would use
to run the
'mutual' command on the file 'data2.first250sec'
in the 'Downloads' directory and put the 'answer' in that directory.
Modify as appropriate:
user@cucsvm:/usr/lib/tisean
./mutual ~/Downloads/ps8data/data2.first250sec o ~/Downloads/ps8data/answer
 If you want to install TISEAN on your own machine, these helpful hints regarding installing and using
it and Mac OSX 10.5
binaries may be useful. I don't have binaries for later versions
of Mac OSX; please let me know if you find (or produce) them so I can
post them here for others to use.
 There are lots of other references and resources for this problem
set in the "interesting links" section below, including a link to the
TISEAN home page.
 Problem Set 9 : Lyapunov exponents.
The following materials may be useful to you as
you do this problem set:
 Problem Set 10 : fractal dimension.
Click here for a detailed list of
the assigned reading for this topic
and here for a scan of
some of that reading (pp166191 of Parker & Chua).
 Problem Set 11 : playing with bike
wheels, writing Lagrangians, and starting to explore the twobody
problem for a binary star. This material is covered in the first few
sections of the classical mechanics notes listed below. Click here for a picture defining true
anomaly,
here for an interactive simulator that you can use to explore
orbits, and
here for a wonderful lecture on dynamical toys like tops and
rattlebacks.
 Some hints about
presentations.
 Problem Set 12 : integrating the
twobody equations. See section 4 of the classical mechanics notes
listed below. Here's an interesting
link that Kristine Washburn found about a variant of this problem.
You may also wish to check out the nbody section of Colonna's webpage
(listed below). Here is the "Chaos
Hits Wall Street" article that's on the reading assignment.
 Problem Set 13 : integrating the
threebody equations for a binaryfield star collision. See section
4.2 of the classical mechanics notes listed below. The "visualization
of dynamical systems" page in the "interesting links" list below has
source code for a lovely visualization of this problem.
Liz's videos and written materials:
Some useful and/or interesting links: (caveat emptor!)
 Henri Poincare didn't only play a formative role in the
foundation of the field of nonlinear dynamics. Among other things, he
came up with the theory of relativity and wrote down e=mc^2 before
Einstein did. Read a bit about
him here.
 The Fyre tool for producing
artwork based on histograms of iterated chaotic functions ,
written by an alumnus of this course.
 Michael Skirpan's
fractal tree generator (= the mother of all solutions to PS3).
 Harold Hausman's
pendulum phase portrait animation .
 You can find a nice animation of the double pendulum (and code to
build animations of other things) here.
 CU's
site license for Matlab now covers student computers! Here's a pdf that describes the
download/licensing process.

The
visualization of dynamical systems page from the Nonlinear
Dynamics and Time Series Analysis Group at the Max Planck Institute
for the Physics of Complex Systems.
 xkcd's take on chaos
 Video recordings of the lectures from Steve
Strogatz's introductory course on nonlinear dynamics and chaos
 Complexity, the flip side of
chaos: complex
dynamics of a flock of starlings. Here's
the Vimeo version of that
video if you prefer that channel.
 Movies of metronomes synchronizing (modernday equivalent of
Huyghens' pendulum clocks): an array of five
and an
array of 32 (!)
 The
PhET project, an interactive simulator that you can use to explore
all sorts of interesting systems. Click on "Play with sims" and go to
"Physics" for the nbody simulator (called "My Solar System").

Modes of a drumhead (try this at home by filling your sink with a few inches of water and then turning on the garbage disposal)
 Analog computers for nonlinear dynamical systems: the Antikythera
mechanism and the digital
orrery (built by Liz's advisor)
 "Guide to
Takens' Theorem" paper (heavy going, mathematically, but very
comprehensive).
 Rigid body
dynamics in zero gravity on the international space station.
 Google labs' Julia
Map website, which uses the Google Maps API (!) to render
fractals. (This site still exists, according to search engines, but
it seems to be offline Liz 12/22/16. Check back again.) The process
is
explained
here.
 A youtube video about
controlling inverted pendula, both single & double.
 Jim Roberge's fabulous
lectures about control theory (RIP, wonderful mentor).
 An applet that
simulates the Lorenz equations, allowing you to enter initial
conditions with a mouse click.
 A gorgeous youtube video that zooms in on the
Mandelbrot set.
 Another 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).
 The
TISEAN timeseries analysis toolkit. The TISEAN site has binaries
for UNIX & windows. 'brew install tisean' works on Macs if you're a
brew user. Here are some examples of
how to run all of this from MATLAB.
 Chaos in the path of a Roomba
 The
Google Books link to the Strogatz text
 Chaotic music & dance stuff:
 NASA's movie of
Hyperion tumbling
 Remember that wonderful
"powers of ten" video from highschool physics?
 SIAM's dynamics
tutorials, many of which were contributed by grad students in courses
like this one.
 The Myphysicslab site,
which contains Java simulations of various interesting dynamical
systems.
 Wolfram's Mathworld site.
 The
FAQ for sci.nonlinear. A fabulous resource.
 The Santa Fe Institute,
which has a couple of
great educational programs for graduate students (the Complex
Systems Summer School) and undergraduates (called "Research
Experiences for Undergraduates").
 NIST's Guide to
Available Mathematical Software
 The Numerical Recipes webpage
 Some Java
demos developed by Michael Cross, who teaches the CSCI4446equivalent
course at Caltech.
 The Chaos
Hypertextbook
 Helwig Hauser's visualization
of dynamical systems page. The pages above that are interesting,
too.
 JeanFrancois Colonna's
"virtual spacetime travel" page, which includes lots of stuff
about the Lorenz system, pendula, the nbody problem, etc. Very nice
graphics.
 Some sources of economic and other time series data: