Timeline for Solutions of the vector field $D=A\frac{\partial}{\partial X}+B\frac{\partial}{\partial Y}$ with $A,B\in k[[X,Y]]$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2022 at 20:40 | comment | added | b.b | Hello, the author of the paper shows under certain assumptions that starting from solutions of $Ady=Bdx$, you can obtain solutions of $D=A\frac{\partial}{\partial X}+B\frac{\partial}{\partial Y}$ at $(0,0)$ (and vice versa). It just happens that when you write the proof, you don't find an $F$ such that $A\frac{\partial F}{\partial X}+B\frac{\partial F}{\partial Y}$ is exactly zero, it is only a multiple of $F$. | |
| Feb 16, 2022 at 16:34 | comment | added | Ilia | I am just curious, what is the reason they add $\text{mod }F$ there? For example, in the case $A=1$, $B=0$ I would expect the solution to satisfy $F_x =0$ but instead we get $F_x$ is proportional to $F.$ | |
| Feb 16, 2022 at 13:19 | history | edited | YCor |
edited tags
|
|
| S Feb 16, 2022 at 13:16 | review | First questions | |||
| Feb 16, 2022 at 13:20 | |||||
| S Feb 16, 2022 at 13:16 | history | asked | b.b | CC BY-SA 4.0 |