Timeline for Dynamical analogue of Morse theory
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2023 at 6:15 | vote | accept | Ali Taghavi | ||
| Jul 28, 2023 at 11:02 | comment | added | Thomas Rot | See for example the discussion in Weinstein's On the hypotheses of Rabinowitz' periodic orbit theorems | |
| Jul 28, 2023 at 10:59 | comment | added | Thomas Rot | I use the following fact: If $N$ is a regular level set of two different Hamiltonians $H_1$ and $H_2$, then the dynamics on $N_1$ with respect to $H_1$ is a rescaling of the dynamics of $H_2$ on $N$. | |
| Jul 28, 2023 at 10:34 | comment | added | Ali Taghavi | My +1 and thanks for your attention to my question and your answer. I think some thing is missing. It seems that you actually use the following statement but I think it is not true: "If $N$ is codimension one submanifold and $H_1$ and $H_2$ are constant on $N$ then the two Hamiltonian flow are the same on $N$" . This is not true for example put $N=$ unit circle in the plane, $H_1\equiv 0$ and $H_2=x^2+y^2-1$ The first Hamiltonian consist of singularities and the second one consist of a periodic orbit, two different dynamic. Am I missing some thing? | |
| Jul 28, 2023 at 8:58 | history | answered | Thomas Rot | CC BY-SA 4.0 |