The zoom link for the first two weeks' worth of lectures
is here. I sent
out the passcode in my bulk email to the class distrib list on 5 Jan.
I'll also post the url and the passcode in the Canvas "announcements"
section.
The zoom link for my office hours
is here. If you
don't see me when you connect, please call my office line (303 492
5355) and remind me to fire up zoom. Set office hours are tuesdays
from 12pm and wednesdays from 2:303:30pm. (I do have a couple of
conflicts with those times, so it's a good idea to check
my main webpage before
schlepping up to my office.) I'm happy to meet at other times as
well; please email me to set up a time.
Finally: the monday help hours (9:3011:30am) will start on 24 January
in ECCS
114B. Here is
the zoom link for those sessions. Please be aware that inperson
visitors will be prioritized if there are simultaneous arrivals.

General information and administrivia

A version of CSCI 4446/5446 is available through
the Complexity Explorer
MOOC platform housed by the
Santa Fe Institute. We'll be supplementing the oncampus
course with some of these materials this spring. These MOOC materials
may be useful to you in other ways as well, especially if you have to
miss a lecture. Please go to that website, register for the course
(which is called
"Nonlinear Dynamics: Mathematical and Computational Approaches"),
and look around a bit (including through the "supplementary
materials" page).

Problem Set 1: logistic map. You can use the logistic map app on
the Complexity Explorer MOOC to check that your solutions are correct
(look in the "supplementary materials" tab). Also, you may wish to
take some time this week to review section 1 of the ODE notes listed
below ("Liz's written notes and videos") if your knowledge of
differential equations is at all rusty.
 Problem Set 2: bifurcation diagrams
and Feigenbaum's constant. Again, you can use the Complexity Explorer
logistic map app mentioned above to check your solutions.
 Problem Set 3: fractals. For some
examples of fractals in the wild,
click
here or
here.

Final
Project Guidelines: you can find tech reports that compile
projects from some previous
semesters here.
Search for the title "Projects in Chaotic Dynamics..."

Problem Set 4: RungeKutta and the driven pendulum equations.

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:

Final Project Details

Problem Set 6: Poincare sections.

Problem Set
7: variational equation. See the notes listed below
("Liz's written notes and videos").

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 PS79 ("Reading assignments for
timeseries analysis")

Instructions on getting the data for this problem set
and
an example of how to embed a data set .
 The
TISEAN timeseries analysis toolkit is available in our cloud IDE
at https://coding.cs.colorado.edu via JupyterHub. This is the
recommended method for accessing these binaries, as they are already
precompiled and ready for use. Login with your CU Credentials and
select the "4446/5446 Chaotic Dynamics" tile to get started. (If you
do not have a stable internet connection, the offline option is to use
the CU CS Foundations Virtual Machine which also has the precompiled
binaries. https://foundation.cs.colorado.edu/vm)
 If you want to install TISEAN on your own machine,
these
helpful hints regarding installing and using it and this link to
the pytisean wrapper
on github may be useful. 'brew tap brewsci/science' followed by
'brew install tisean' has worked in the past on Macs if you're a brew
user, but leaves the commands prefaced by a '' ... i.e.,
'tiseanmutual'.

Jay Kominek's mpeg movie of what happens as you change tau in
embeddings of data from the Lorenz system.
 There are lots of other references and resources for this
problem set in the "interesting links" section below.

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). You can download a pdf of the whole book from the
CU Libraries, but you'll need to be on a campus network (or the
VPN). Here is
a jpg
of the Hunt & Sullivan proof.

Some hints
about presentations.

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
("Liz's written notes and videos").
Click
here for a picture defining true anomaly
and here
for a wonderful lecture on dynamical toys like tops and rattlebacks.

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.