The eccentric annular billiard, or how to mix a Pan Galactic Gargle Blaster
Channel: Nils Berglund
Date: 2021-05-12

The two circles forming this annular billiard do not have the same center. The inner circle has been moved a little bit to the right, compared to a perfect annulus. The reason is that if both circles were concentric, conservation of angular momentum would make the billiard regular (or integrable, in more technical terms). Here we have a mixed billiard, somewhat similarly to the lemon-shaped billiard shown here: https://youtu.be/SGf-sbrLL7A - some trajectories only collide with the outer circle, and their dynamics is regular. At least part of the trajectories colliding with both circles are chaotic, which is manly due to the dispersing effect of the inner circle's concave boundary.

Music: "You are my rainbow", by Unicorn Heads@UnicornHeads

Current version of the C code used to make these animations: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html

Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)