Timeline for Ergodicity of a dynamical system on the $n$-sphere
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2020 at 18:41 | comment | added | Qiaochu Yuan | $S^1$ acts freely and smoothly on every odd sphere $S^{2k-1}$ (regarded as the unit sphere in $\mathbb{C}^k$, with the action given by scalar multiplication) so generates a nowhere-vanishing vector field whose flow is very much non-ergodic. | |
| Oct 3, 2020 at 18:06 | comment | added | Christian Remling | But there's no reason why specifically Lebesgue measure would be invariant. For example, you can move fast through some regions of $S^1$ and slowly through others. | |
| Oct 3, 2020 at 16:26 | comment | added | G. Panel | 1) Ergodic with respect to the Lebesgue measure. 2) I take a look a that, thank you! | |
| Oct 3, 2020 at 16:17 | comment | added | D. Thomine | 1) Ergodic with respect to which measure? 2) Beware of the Hopf fibration. | |
| Oct 3, 2020 at 15:26 | history | asked | G. Panel | CC BY-SA 4.0 |