Timeline for Given a vector field all of whose integral curves are closed, is the period a smooth function?
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| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
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| Aug 30, 2012 at 7:04 | history | edited | agt | CC BY-SA 3.0 |
I pointed out that the original question has two parts and the first one has been answered (negatively).
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| Aug 29, 2012 at 19:48 | answer | added | Alejandro | timeline score: 7 | |
| Aug 6, 2012 at 18:40 | answer | added | Sam Lisi | timeline score: 5 | |
| Aug 6, 2012 at 15:37 | history | edited | agt | CC BY-SA 3.0 |
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| Aug 6, 2012 at 14:55 | history | edited | agt | CC BY-SA 3.0 |
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| Aug 6, 2012 at 9:59 | answer | added | Sebastian | timeline score: 4 | |
| Aug 6, 2012 at 8:44 | history | edited | agt | CC BY-SA 3.0 |
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| Aug 6, 2012 at 8:25 | comment | added | agt | @Thomas Rot thank you, so with the harmonic oscillator, we find a Hamiltonian system all of whose orbits are periodic for which $\tau$ is not smooth and $\text{per}_H$ is not a smooth manifold. But then what hypothesis are behind the statement in Guillemin and Sternberg ("when all orbits are periodic, we can take $N=\text{per{$ in Weinstein's formulation of the energy-period relation)? But probably I should restrict to periodic motions with positive period. | |
| Aug 6, 2012 at 8:00 | comment | added | Thomas Rot | A random thought: What about a harmonic oscillator? The periods are constant non-zero, except for the equilibria. But maybe you want to avoid this. | |
| Aug 6, 2012 at 7:44 | history | edited | agt | CC BY-SA 3.0 |
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| Aug 6, 2012 at 7:38 | history | edited | agt | CC BY-SA 3.0 |
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| Aug 6, 2012 at 7:19 | history | asked | agt | CC BY-SA 3.0 |