Timeline for Planar flow with bounded orbits and a single equilibrium point
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2021 at 21:33 | comment | added | Martin M. W. | @WillieWong Nice, I edited the post to add your argument. | |
| Apr 6, 2021 at 21:32 | history | edited | Martin M. W. | CC BY-SA 4.0 |
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| Apr 6, 2021 at 15:32 | vote | accept | coudy | ||
| Apr 6, 2021 at 15:32 | comment | added | coudy | @Wong Indeed, that works, perfect. | |
| Apr 6, 2021 at 15:27 | comment | added | Willie Wong | @coudy: what if you remove the normalization step? The construction of $T$ is the same. Let $\bar{B}$ be the closed ball of radius 1. The argument above shows that the whole space must be contained in the image of $[0,T]\times \bar{B}$, but the latter is compact. | |
| Apr 6, 2021 at 8:52 | comment | added | coudy | Indeed that works in the $C^1$ case. I am wondering if that argument can be adapted to the $C^0$ setting. | |
| Apr 6, 2021 at 0:52 | comment | added | Martin M. W. | Good point! I edited accordingly. | |
| Apr 6, 2021 at 0:51 | history | edited | Martin M. W. | CC BY-SA 4.0 |
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| Apr 6, 2021 at 0:37 | comment | added | Willie Wong | technical quibble: if $\lim_{t\to -\infty} \varphi_t (x) = 0$ for all $x$, then $O_t = \mathbb{R}^2$ for all $t$ as you defined it. You probably want $0 < s < t$ in the definition. | |
| Apr 5, 2021 at 23:23 | history | edited | Martin M. W. | CC BY-SA 4.0 |
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| Apr 5, 2021 at 22:18 | history | answered | Martin M. W. | CC BY-SA 4.0 |