Correction to Problem Sheet 3

There was a misplaced sign (relative to the parentheses) in problem 3. That has now been corrected.

Solution Sheet 2 posted

Solution sheet 2 is now posted. Let me know if you have any questions or if you've found any typos.

New Paper on Period Doubling Cascades and Chaos

The timing of this paper is excellent, as we've been discussing it in lecture. This new paper by Evelyn Sander and Jim Yorke is a (mostly) expository paper about the period doubling route to chaos. It includes some of the pictures that I mentioned but was unable to draw, and it also relates what we've seen in maps to what we have seen a bit (problem 5 on homework sheet 2) and what we will see more in flows. I don't recommend a cover-to-cover reading, but I think a perusal of relevant parts of the paper could be helpful.

Another Typo Correct in Homework Sheet 2

I have corrected equation (11) in homework sheet 2. The third term in the second equation of (11) should have (theta_3 - theta_2) as an argument for the sine instead of the (theta_2 - theta_3) that was there before. If you tried with the old version, you'll notice that the change of variables won't quite work.

This sheet was a bit buggy with typos. Sorry about that.

Solution Sheet 1 posted

I've posted the solutions for problem sheet 1.

Lecture Notes posted up through page 55

I have now posted the lecture notes through page 55. This finishes the notes except for the 'other topics', which have not been determined yet and won't be for a while. (Please let me know if there are any that particularly interest you.) I won't create those notes until the very end.