Timeline for Flat Riemannian metrics adapted to quadratic vector fields with center
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Dec 5, 2017 at 12:38 | history | bounty ended | CommunityBot | ||
| S Dec 5, 2017 at 12:38 | history | notice removed | CommunityBot | ||
| S Nov 27, 2017 at 10:54 | history | bounty started | Ali Taghavi | ||
| S Nov 27, 2017 at 10:54 | history | notice added | Ali Taghavi | Draw attention | |
| Jul 24, 2017 at 11:51 | comment | added | Malkoun | Let us continue this discussion in chat. | |
| Jul 24, 2017 at 11:34 | comment | added | Ali Taghavi | @Malkoun If i am not mistaken you are interested in the problem of "Completeness" or Non completeness of polynomial vector fields(Of degree 2). Yes? If it is the case, I think the following paper completely classify such vector fields sciencedirect.com/science/article/pii/0022039686901130/… | |
| Jul 24, 2017 at 11:28 | comment | added | Malkoun | Ok. My interest in these quadratic vector fields was from another point of view. I wanted to find such vector fields for which the flow never blows up in finite time. They are rare but they exist. I suppose one may try to classify the quadratic vector fields vanishing at the origin, maybe under some assumptions, but this is a very tedious way to approach the problem you are interested in. Perhaps a less brute-force approach would be desirable, such as the one you are attempting. | |
| Jul 24, 2017 at 11:20 | comment | added | Ali Taghavi | @Malkoun But I am (almost) sure that the problem is open even for n=2 (quadratic vector field). | |
| Jul 24, 2017 at 11:18 | comment | added | Malkoun | I don't know. I haven't been following the literature surrounding this problem. | |
| Jul 24, 2017 at 11:13 | comment | added | Ali Taghavi | Sorry I revise the comment ....H(2) is finite or no? | |
| Jul 24, 2017 at 10:57 | comment | added | Ali Taghavi | @Malkoun Thank you for your comment. While a homogeneous quadratic vector field does not have a limit cycle, but I think that the problem for a general quadratic system is still open.That is it is open to decide whether $H92)$ is finite or no? | |
| S Jul 24, 2017 at 1:23 | history | suggested | jeq | CC BY-SA 3.0 |
Corrected some English typos.
|
| Jul 24, 2017 at 1:17 | review | Suggested edits | |||
| S Jul 24, 2017 at 1:23 | |||||
| Jul 23, 2017 at 19:21 | comment | added | Malkoun | I find it surprising, and highly interesting, that problems concerning polynomial vector fields in dimension 2, which are vector fields that can each easily be drawn, remain open to this date. I am not very familiar with the literature, but I know that Date had classified the homogeneous quadratic fields in dimension 2. Perhaps the quadratic vector fields vanishing at the origin have also been classified by now? I mean, in principle, you are only adding a linear vector field to the homogeneous quadratic one, but I suspect the classification to be very tedious. Just a small question/comment. | |
| Jul 23, 2017 at 19:01 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
deleted 2 characters in body
|
| Jul 23, 2017 at 18:46 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 79 characters in body
|
| Jul 23, 2017 at 18:37 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
deleted 57 characters in body
|
| Jul 23, 2017 at 18:31 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 340 characters in body
|
| Jul 23, 2017 at 18:10 | history | asked | Ali Taghavi | CC BY-SA 3.0 |