Timeline for Logistic sequence convergence
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2021 at 9:15 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Mar 7, 2021 at 6:55 | comment | added | Gerry Myerson | You waited less than half-a-day for your post on m.se to get an answer. It's recommended to wait several days before giving up on m.se to post here. Anyway, I have posted an answer there, as I think that's a more appropriate site for the question. | |
| Mar 7, 2021 at 6:46 | vote | accept | Bogdan | ||
| Mar 7, 2021 at 6:44 | answer | added | Robert Israel | timeline score: 1 | |
| Mar 7, 2021 at 6:32 | comment | added | Bogdan | Imply convergence if the initial data is close to the fixed point (or if the sequence come close that point at some $n$). But in general I don't see why stable fixed point imply convergence. Do you know a proof for that? | |
| Mar 7, 2021 at 6:30 | comment | added | Gerry Myerson | In the earliest of the three stackexchange posts, the user gives the formula for the fixed point, and the reason for its stability for $1<r<3$. A stable fixed point implies convergence to that fixed point, so it seems to me that what you want (for your first question) is already there. | |
| Mar 7, 2021 at 6:06 | comment | added | Bogdan | Practically I want some technical details about the proof of convergence (not the existence of 2,3-cycles). I studied a lot the problem and I know it's interesting story. But I cannot figure out even in these simple cases how to prove the convergence to the same values for any starting point $a\in (0,1)$. | |
| Mar 7, 2021 at 5:58 | comment | added | Bogdan | I will see the video. I understand what you say but it's not clear for me... | |
| Mar 7, 2021 at 5:44 | comment | added | Bogdan | Where I can find a proof that it is indeed convergence on those points with $g'(x)<0$ no matter what is our choice of the starting value $a$? So we can take $a$ some distance apart from $x$. | |
| Mar 7, 2021 at 5:29 | history | asked | Bogdan | CC BY-SA 4.0 |