Timeline for Do there exist small neighborhoods in a classical mechanical system without pairs of focal points?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2010 at 4:34 | comment | added | Theo Johnson-Freyd | I'll definitely come up and we can talk. What days are good? | |
| Feb 9, 2010 at 2:48 | comment | added | Richard Montgomery | Theo: I am up at MSRI till June: schedule to come by via email and we can talk about what you are doing if you like | |
| Feb 8, 2010 at 18:46 | comment | added | Theo Johnson-Freyd | Anyway, I've thought a lot about the harmonic oscillator --- it's the only one I can solve explicitly --- and maybe I misphrased my question. But the point is that for a small open neighborhood O = O_0 = O_1, for any q_0,q_1 \in O, for any \epsilon < 2\pi, there is a unique path connecting q_0 to q_1. Fixing O and letting \epsilon \to 0, the path of duration \epsilon starting stationary at q\in O certainly ends in O, and so is one of the paths in my family. So this is not a counterexample. I believe that any counterexample must include a potential that grows \gg q^2. | |
| Feb 8, 2010 at 18:44 | comment | added | Theo Johnson-Freyd | I corrected some minor formatting. Annoyingly, Markdown interprets back ticks differently from the way TeX does. | |
| Feb 8, 2010 at 18:38 | history | edited | Theo Johnson-Freyd | CC BY-SA 2.5 |
corrected formatting
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| Feb 8, 2010 at 8:16 | history | answered | Richard Montgomery | CC BY-SA 2.5 |