(ChaosBook.org blog, chapter Billiards) — Predrag Cvitanovic 2009-02-11 12:55

Now go forth and play billiards — John F. Gibson, 2009-02-12 17:27

Mason A Porter 2010-02-14 I'm going through this because I am writing up a solution to a problem that follows this derivation. I have asked my students to derive the Jacobian for billiards in problem 7 of homework 3, which is on maps, in my class. The website for the class is nonlinear2010.blogspot.com

Predrag 2010-02-14 Great. The chapter needs some loving care, formulas like those of Example 8.1 (3-disks) are a bit stupid. Please use my internal version, perhaps more useful for this purpose. Students should also understand the next chapter, “World in a mirror,” doing dynamics on the fundamental domain is much smarter than dynamics without desymmetrization. Good problems and solutions we could add to ChaosBook exercises/solutions.

Mason A Porter 2010-02-14 Immediately in line below equation (8.6): You are missing two “^+” superscripts. Predrag 2010-02-14 I made the editorial decision to mark only “^-” superscripts. If you think it is confusing, I can add throughout “^+” superscripts, but it ain't pretty…

Mason A Porter 2010-02-14 In equ (8.11), it should be k = 1 in the bottom and n_p on top (unless you are purposely going against that convention). Predrag 2010-02-14 Otherwise one would be tempted to multiply the wrong way. Now I say “The unconventional product limits are a reminder that the product is time-ordered, with later times corresponding to multiplication from the left, as in (4.52), AKA equ label {jacoB}.”

Mason A Porter 2010-02-14 You switch back and forth regarding kth and nth collisions and it would be better to be uniform. Predrag 2010-02-14 Historical - cycle length is n so sums up n were labeled by k. But I can see it is not necessary - fixed now.

Mason A Porter 2010-02-14 You refer to a “velocity” of 1 rather than a “speed” of 1 on several occasions. Predrag 2010-02-14 thanks, fixed.

~~DISCUSSION~~