Timeline for Question on Banyaga's theorem
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2022 at 10:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 9, 2022 at 9:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 10, 2022 at 8:53 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jul 10, 2022 at 8:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 25, 2016 at 1:11 | comment | added | mme | He said the group generated by autonomous Hamiltonians. There's no reason to believe the product is autonomous. Then the interesting result is that you can express any Hamiltonian diffeomorphism as the composition of finitely many autonomous Hamiltonian diffeomorphisms. | |
| Nov 24, 2016 at 22:45 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 25, 2016 at 21:56 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 25, 2016 at 23:07 | comment | added | PVAL | If I recall correctly, the set of autonomous Hamiltonians is closed under conjugation from any element of $\mbox{Ham}$. So by a theorem of Banyaga ($\mbox{Ham}$ is simple), any time there is a non-autonomous Hamiltonian, the set of autonomous ones fail to be a group. | |
| Sep 25, 2016 at 19:19 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 26, 2016 at 17:42 | answer | added | augustin banyaga | timeline score: 1 | |
| Aug 26, 2016 at 16:20 | comment | added | Thisquestionisreallyhard | I will try to understand those answers. If I may, here is a link to some notes from Banyaga: personal.psu.edu/auw4/dakar.pdf He defines $\mathcal H$ on page 1 as the group of time 1 autonomous Hamiltonian diffeomorphisms, and $\mbox{Ham}$ as the group of all Hamiltonian diffeomorphisms on page 5. The Corollary on page 7 claims that, for a compact manifold, these two are the same. I don't think I am misunderstanding the statement, and Banyaga is apparently an expert in the field. What is the issue? | |
| Aug 26, 2016 at 8:12 | comment | added | Peter Michor | A similar negative answer is in mathoverflow.net/a/18801/26935 | |
| Aug 26, 2016 at 7:40 | comment | added | Peter Michor | This answered (in the negative for many symplectic manifolds) in mathoverflow.net/a/41092/26935 | |
| Aug 26, 2016 at 5:15 | history | asked | Thisquestionisreallyhard | CC BY-SA 3.0 |