3 ms·
I believe that if the runners speeds are all real numbers which are linearly independent over the rationals, then the associated dynamical system will be ergodi
by impendia 4y ago
I believe that if the runners speeds are all real numbers which are linearly independent over the rationals, then the associated dynamical system will be ergodic
https://en.wikipedia.org/wiki/Ergodicity https://en.wikipedia.org/wiki/Ergodicity
and what you say is true.
But in addition to your example you have to worry about, e.g. sqrt(2), sqrt(3), and sqrt(2) + sqrt(3).
- contravariant 4y agoI agree that it's probably ergodic, but to show every distribution will definitely come about (approximately) you'll need a slightly stronger property than just ergodicity. Ergodicity guarantees it is almost always the case, but if you want it to always be the case you'll need it to be uniquely ergodic. Since irrational rotations are uniquely ergodic I reckon this system will also be, but I think the proof won't be trivial.