Timeline for Given a vector field all of whose integral curves are closed, is the period a smooth function?
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| Aug 30, 2012 at 6:43 | comment | added | agt | Initially I tried to justify the statement in Sternberg-Guillemin along the lines of Sebastian's answer. But it wasn't conclusive. Then I devised the very elementary counter-example in the Edit after which in general $\tau$ is not even continuous. So, under what hypothesis Guillemin and Sternberg state (between pages 170-171) that $\mathrm{per}_H$ is submanifold of $\mathbb R\times M$? I have thought to the presence on $M$ of a principal $S^1$-bundle structure whose fibers are the orbits of $X.$ But it seems to strong. | |
| Aug 29, 2012 at 19:48 | history | answered | Alejandro | CC BY-SA 3.0 |