Timeline for Inverse Problem for jet equations
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2012 at 20:28 | vote | accept | Nevermind | ||
| Feb 27, 2012 at 13:45 | answer | added | Deane Yang | timeline score: 2 | |
| Feb 26, 2012 at 22:41 | answer | added | Nevermind | timeline score: 0 | |
| Feb 26, 2012 at 22:11 | comment | added | Nevermind | Please note that this is NOT about solving the jet equations! The question is of different nature: The jet equation is supposed to hold. Here it is about the associated function equation. I think tat wasn't clear. | |
| Feb 26, 2012 at 22:08 | history | edited | Nevermind | CC BY-SA 3.0 |
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| Feb 26, 2012 at 22:05 | comment | added | Nevermind | Ok.. Now I see whats the problem here. I made a mistake in writing the question! Sorry for that. Please read the second example again, I changed it. | |
| Feb 26, 2012 at 17:36 | comment | added | Deane Yang | Willie, indeed. There's no work to be done here. Everything being asked follows directly from the definition of a jet. | |
| Feb 26, 2012 at 17:11 | comment | added | Deane Yang | Nevermind, please write out the details in co-ordinates and show us where you get stuck. I'd be happy to help with that. | |
| Feb 26, 2012 at 16:14 | comment | added | Willie Wong | Aren't you done once you solve the matrix equation? By taking local coordinates you reduce to considering maps between Euclidean spaces and since you are only looking at $j^1$ you just need to consider linear maps, which are uniquely determined by their derivative at the origin. | |
| Feb 26, 2012 at 15:54 | history | edited | Nevermind | CC BY-SA 3.0 |
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| Feb 26, 2012 at 15:45 | comment | added | Nevermind | @Deane: Suppose we have the matrix equation (what is really the same thing as the jet equation), then what? How to get to the function equations? Some sort of partial differential equation solving process? Please point me to how to get from the Jacobi matrix level (the infinitesimal level) to the local level | |
| Feb 26, 2012 at 15:42 | comment | added | Nevermind | @dverietti: That only applies to the first example and as I said that is an easy situation. Nevertheless this is not really an argument for situations like the second example. | |
| Feb 26, 2012 at 15:35 | comment | added | Deane Yang | diverietti is, of course, right. $j^1_mf$ is by definition an equivalence class, and you can't have an empty equivalence class. But you might as well write all the "matrix equations" out explicitly and write down explicit formulas for everything. By the way, presumably you know the answer when $M$ and $N$ are 1-dimensional, right? | |
| Feb 26, 2012 at 15:16 | comment | added | diverietti | Maybe the answer is even easier... By definition you have a representative for $j^1_mf$ in some small neighborhood $U$ of $m$. Since $j^1_mf=j^1_mg$, just take the same representative for $g$. | |
| Feb 26, 2012 at 14:42 | comment | added | Nevermind | Don't see how this will help. In local coordinates the jet equations are 'matrix equations' involving the Jacobi-matrices. But I still can't see how this lifts to the function equations. Can you give a little more details please? | |
| Feb 26, 2012 at 12:19 | comment | added | Deane Yang | Way too much abstraction here. You're talking about one point and a neighborhood of it. Do everything in local co-ordinate, and it's all very easy and clear. You can't answer this question without using the actual definition of a "jet". | |
| Feb 26, 2012 at 11:59 | history | asked | Nevermind | CC BY-SA 3.0 |