Timeline for Can every ergodic map be approximated by ergodic maps close to the identity?
Current License: CC BY-SA 4.0
24 events
| when toggle format | what | by | license | comment | |
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| S Apr 18, 2021 at 5:57 | history | bounty ended | CommunityBot | ||
| S Apr 18, 2021 at 5:57 | history | notice removed | CommunityBot | ||
| Apr 11, 2021 at 7:50 | vote | accept | Nate River | ||
| Apr 11, 2021 at 6:36 | answer | added | Anthony Quas | timeline score: 2 | |
| Apr 11, 2021 at 6:13 | history | edited | Nate River | CC BY-SA 4.0 |
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| Apr 11, 2021 at 6:13 | comment | added | Nate River | Ah damn I always forget the absolute values. Yes, thanks! | |
| Apr 11, 2021 at 6:06 | comment | added | Anthony Quas | Do you want absolute values in your condition, I think $\int (g\circ T-g\circ F)\,d\mu=\int (g-g)\,d\mu=0$. | |
| Apr 10, 2021 at 4:03 | history | edited | Nate River | CC BY-SA 4.0 |
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| Apr 10, 2021 at 3:48 | history | edited | Nate River | CC BY-SA 4.0 |
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| S Apr 10, 2021 at 3:22 | history | bounty started | Nate River | ||
| S Apr 10, 2021 at 3:22 | history | notice added | Nate River | Draw attention | |
| Apr 6, 2021 at 22:51 | comment | added | Nate River | Yeah that’s right. | |
| Apr 6, 2021 at 19:33 | comment | added | Jochen Glueck | In the formula for $\delta$-close, do you mean the composition $g \circ T$ by the notation $Tg$? | |
| Apr 6, 2021 at 15:06 | review | Close votes | |||
| Apr 10, 2021 at 3:25 | |||||
| Apr 6, 2021 at 8:30 | comment | added | Nate River | Let us continue this discussion in chat. | |
| Apr 6, 2021 at 8:22 | comment | added | Leo Moos | Sorry about that - after two missteps I should probably refrain from making any more attempts. However, I can't resist suggesting you try permuting two different enough ergodic maps $T_1,T_2$ on some $Y$ via $T(y,1) = (T_1(y),2)$ and vice-versa on $Y \times \{ 1, 2 \}$. Perhaps the $T_i$ could be rotations of $Y = \mathbf{S}^1$ through suitably chosen irrational angles? | |
| Apr 6, 2021 at 8:10 | comment | added | Nate River | Hm this wouldn’t be ergodic would it? | |
| Apr 6, 2021 at 8:03 | comment | added | Leo Moos | Whoops, I missed that - my bad. Regardless, what if $X = [0,1] \times \{1,2 \}$ and $T$ is the permutation sending $[0,1] \times \{ 1 \}$ to $[0,1] \times \{ 2 \}$ and vice-versa? | |
| Apr 6, 2021 at 8:00 | comment | added | Nate River | No atoms sir... | |
| Apr 6, 2021 at 7:58 | comment | added | Leo Moos | What if $X = \{ 1,2 \}$ and $T$ is the permutation $(1 \, 2)$? | |
| Apr 6, 2021 at 7:48 | history | edited | Nate River | CC BY-SA 4.0 |
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| Apr 6, 2021 at 7:45 | comment | added | Nate River | Oh damn you’re right.. what kind of distance do I want.. | |
| Apr 6, 2021 at 7:07 | comment | added | D. Thomine | If $T$ and $F$ are measure-preserving, doesn't this mean that $T\mu=F\mu=\mu$? | |
| Apr 6, 2021 at 6:00 | history | asked | Nate River | CC BY-SA 4.0 |