Timeline for Motivation behind the usual setting of the (weak) Arnold conjecture for fixed points of an hamiltonian diffeomorphism
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2022 at 16:43 | comment | added | Riccardo | @JonnyEvans That paper is quite nice to read! It reads like a script, thanks a lot for sharing it! | |
| Feb 14, 2022 at 8:24 | comment | added | Jonny Evans | In the title you mention the motivation for the conjecture. If you want to read a very beautiful paper of Arnold which explains the thinking/philosophy behind some of his conjectures, try his "Topological problems in wave propagation and topological economy principle in algebraic geometry". | |
| Feb 14, 2022 at 0:10 | comment | added | Will Sawin | I don't know if the idea was inspired by physics, but physicists are certainly interested in states of systems that are stable for a long time - for example because they make it easy to predict what will happen for a long time, or because that's where you want to put your satellite, or for a number of reasons. If the Hamiltonian is periodic with period $t$, a fixed point of the evolution for time $t$ map will be stable for a long time, but if the Hamiltonian is not periodic, it won't be. | |
| Feb 13, 2022 at 23:30 | comment | added | Riccardo | @WillSawin that's an interesting observation, thanks for sharing! so we ask for periodicity in order to deal with "meaningful" fixed points? is this idea inspired by physics somehow? | |
| Feb 13, 2022 at 23:22 | comment | added | Will Sawin | If the Hamiltonian is not $1$-periodic, having a fixed point is not so meaningful, as the point will stay fixed after $1$ unit of time but could move over the next $1$ unit. | |
| Feb 13, 2022 at 21:19 | history | asked | Riccardo | CC BY-SA 4.0 |