A billiard ball in a rectangle with two circular ends: slight changes in initial conditions make such a big difference that eventually it could be anywhere. To be precise, we say its motion is "ergodic".
This animation was made by @roice713.
(to be continued) pic.twitter.com/rQPS0OOdXH — John Carlos Baez (@johncarlosbaez) July 28, 2018
For the precise definition of "ergodic" read my diary:https://t.co/kcgMZNahqv
A billiard ball moving in a convex region with smooth boundary can't be ergodic. In fact, in 1973 Lazutkin showed this for a convex table whose boundary has 553 continuous derivatives! — John Carlos Baez (@johncarlosbaez) July 28, 2018
However....
I appreciate the tag and am glad I get to follow this thread now, but also need to correct the attribution - the animation was by Phillipe Roux :) https://t.co/8HVbdDZ2dW — Roice (@roice713) July 28, 2018
