Timeline for When the integrable system defines a moment map?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 10 at 11:07 | comment | added | Robert Bryant | Consider the example of the $2$-sphere with its standard area form as symplectic struture. Now let $F = (f_1):S^2\to\mathbb{R}$ be any non-constant smooth function. I assume that meets your criterion as an integrable system, and the image of $F$ is an interval in $\mathbb{R}$. However, in general the flow of the Hamiltonian vector field on $S^2$ that corresponds to $f_1$ will not be periodic. You need that flow to be periodic or it won't come from a circle action. It's easy to construct higher dimensional examples by taking products. | |
| Aug 9 at 18:43 | comment | added | Michael Hardy | I changed $2n-$dimensional to $2n$-dimensional, fixing this conspicuous typographical error. | |
| Aug 9 at 18:39 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 3 characters in body
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| Aug 9 at 14:07 | history | asked | Nicolas Medina Sanchez | CC BY-SA 4.0 |