Ergoticity

For maximum benefit fun be sure to watch the animation:

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

* * * * *

No particular region of the space is priviliged. No matter where the billiard ball starts, in time it could be anywhere. A bit more exactly (Wikipedia):

In probability theory, an ergodic dynamical system is one that, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states in its phase space. In physics the term implies that a system satisfies the ergodic hypothesis of thermodynamics.