Timeline for Obstruction to the existence of a globally defined integrating factor
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 2, 2020 at 17:01 | vote | accept | KhashF | ||
| Mar 20, 2020 at 19:05 | answer | added | Willie Wong | timeline score: 1 | |
| Mar 20, 2020 at 18:34 | comment | added | Willie Wong | (More precisely, your function $g = \frac{x^2 + y^2}{2xy}$.) | |
| Mar 20, 2020 at 18:29 | comment | added | Willie Wong | In your "counter example", your function $g$ is not smooth. (It is singular whenever $x = 0$ or $y = 0$.) | |
| Mar 19, 2020 at 3:22 | comment | added | KhashF | @WillieWong Well, in that case $\omega$ is not in the form of ${\rm{d}}f$, but why not a multiple of such a thing? For instance, $\omega:=-\frac{y}{x^2+y^2}{\rm{d}}x+\frac{x}{x^2+y^2}{\rm{d}}y$ is famously closed but not exact on $U:=\Bbb{R}^2-\{(0,0)\}$. But it is a multiple of ${\rm{d}}\left(\frac{y^2}{x^2+y^2}\right)$. | |
| Mar 19, 2020 at 3:06 | comment | added | Willie Wong | For non-examples, just take any closed but non-exact $\omega$ on $U$ that fails to be simply connected? | |
| Mar 19, 2020 at 2:36 | history | asked | KhashF | CC BY-SA 4.0 |