Timeline for Do ergodicity, minimality and equicontinuity on a compact space imply total ergodicity?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2015 at 22:52 | vote | accept | Stéphane Laurent | ||
| Aug 5, 2015 at 22:52 | comment | added | Stéphane Laurent | The same trap as here ! Proposition 18.37 is about a measure-preserving group automorphism ! | |
| Aug 5, 2015 at 22:01 | comment | added | Stéphane Laurent | If the fact you mention in the proof of Proposition 18.37 is right, then the conclusion follows from the first assertion of the theorem. No ? | |
| Aug 5, 2015 at 21:52 | comment | added | Stéphane Laurent | Thank you for this remark. You are right, there's a problem somewhere. | |
| Aug 5, 2015 at 21:19 | comment | added | V. Delecroix | very strange... the odometer is for sure minimal (not hard to see), equicontinuous (it is a rotation on a compact group). I do not understand the argument of the last sentence of the proof of the Proposition 18.37 that you mentioned: "the last assertion follows from the fact that $T_\phi$ has nontrivial periodic points if and only if $T_{\phi^k}$ does for some/all $k \in \mathbb{N}$". This fact is right, but I do not see how it proves anything about total ergodicity. | |
| Aug 5, 2015 at 21:08 | comment | added | Stéphane Laurent | I said in the comments that the answer is yes. If you are right, that would mean that theorem 2.11 in Petersen's book is wrong. Are you sure the odometer is minimal and equicontinuous ? BTW I have also shown this result in a different way (actually I posted this question to check my result). | |
| Aug 5, 2015 at 21:03 | history | answered | V. Delecroix | CC BY-SA 3.0 |