Timeline for About the geometry of completely integrable systems
Current License: CC BY-SA 3.0
16 events
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| May 4, 2011 at 19:05 | comment | added | agt | Excuse me for the delay in accepting the answer. I believed to have already accepted it after my last comment. Probably then I clicked twice; the first accepting, and the second time inadvertently to dismiss. My mistake. | |
| May 4, 2011 at 18:48 | vote | accept | agt | ||
| May 4, 2011 at 13:48 | comment | added | DamienC | Thanks for asking the question. It was a pleasure to take a new look at Colin de Verdiere's introduction (it seems that he is not going to write the next chapters). By the way, I have rewritten my answer according to our discussion. | |
| May 4, 2011 at 13:40 | history | edited | DamienC | CC BY-SA 3.0 |
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| May 4, 2011 at 13:35 | history | edited | DamienC | CC BY-SA 3.0 |
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| May 4, 2011 at 13:31 | vote | accept | agt | ||
| May 4, 2011 at 13:31 | |||||
| May 4, 2011 at 13:29 | comment | added | agt | Dear DamienC: Thank you very much, "perhaps" I have realized what I was missing. This dialogue with you was very useful to me. | |
| May 4, 2011 at 13:20 | history | edited | DamienC | CC BY-SA 3.0 |
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| May 4, 2011 at 13:19 | comment | added | DamienC | But the leaves of $\mathcal F$ are not arbitrary: they are precisely level sets of $f_1,\dots,f_n$. | |
| May 4, 2011 at 12:26 | comment | added | agt | Dear DamienC, By the theorem of Carathedory-Jacobi-Lie I am able to extend $f_1,\ldots, f_n$ to a local symplectic chart $f_1,\ldots,f_n,g_1,\ldots,g_n$ around an arbitrary point $x$. So taking level sets of $g_1,\ldots,g_n$, I get a Lagrangian submanifold $\Sigma$ passing through $x$ and transversal to $\mathcal{F}$. But I am unable to exclude that the intersection of $Sigma$ with some leaf of $mathcal{F}$ has $x$ as accumulation point. | |
| May 4, 2011 at 7:43 | history | edited | DamienC | CC BY-SA 3.0 |
expand a bit the answer according to comments; deleted 3 characters in body
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| May 4, 2011 at 7:16 | comment | added | DamienC | Dear Giuseppe. The proof given in the limked Lecture Notes extend to any complete lagrangian leaf $\Lambda$ (without properness assumption) as soon as it does not contain critical points for $F$. So to make the conclusion work one could either say "for almost all $x\in M$". | |
| May 4, 2011 at 5:46 | comment | added | agt | Dear DamienC, thanks a lot for your attention. About the question: my doubt arose just because I was unable to conclude the reported statement, or to construct a counterexample, within the hypothesis in the initial setting. Thanks also for the linked first chapter, surely it will be useful. | |
| May 3, 2011 at 20:07 | history | edited | DamienC | CC BY-SA 3.0 |
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| May 3, 2011 at 19:18 | history | edited | DamienC | CC BY-SA 3.0 |
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| May 3, 2011 at 19:10 | history | answered | DamienC | CC BY-SA 3.0 |