New answers tagged

0 votes

Non-recurrent points of $F(a,b)=(b,ba)$ in a compact metric group $G$

This map is isometric. So the set of recurrent points is closed. (And hence, by Poincaré, every point is recurrent.) Indeed, let $x$ be in the closure of the set of recurrent points and fix $N$ and $\...
  • 52.7k
1 vote

Ergodicity question

It is true that a system is ergodic if (and only if) every measurable function constant along trajectories is globally constant almost everywhere. For indicator functions this is just the usual ...
  • 12.9k

Top 50 recent answers are included