Timeline for An algorithm for Poincare recurrence time
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| May 4, 2017 at 20:50 | comment | added | O. S. Dawg | Very relevant: arXiv:1705.01444v1 | |
| May 15, 2015 at 2:35 | comment | added | O. S. Dawg | More of a comment than an answer: This method, mathforum.org/kb/message.jspa?messageID=7379751, will also find the simultaneous approximations needed to solve your problem. | |
| May 14, 2015 at 10:42 | comment | added | John R Ramsden | Isn't it just a matter of finding sufficiently good rational approximations to $\frac{1}{2 \pi}$, $\frac{\sqrt{2}}{2 \pi}$, $\frac{\sqrt{3}}{2 \pi}$, $\frac{\sqrt{5}}{2 \pi}$, then taking t as their least common denominator? | |
| May 13, 2015 at 8:53 | history | edited | Ian Morris |
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| May 13, 2015 at 1:02 | answer | added | Robert Israel | timeline score: 2 | |
| May 13, 2015 at 0:37 | comment | added | Douglas Zare | One example: $t=32733777552734744709300 \times 17310639413 \times 122447 (2\pi), f(t) = 3.99999999946$. | |
| May 12, 2015 at 20:14 | vote | accept | wdlang | ||
| May 12, 2015 at 20:11 | comment | added | Douglas Zare | It's not too hard to find values "by hand" by which I don't mean by hand, but with only some simple calculations, no lattice reduction. Find really good rational approximations to $\sqrt{2}$, so that you get $p_2-q_2\sqrt{2}$ is small. Then consider good approximations to $\sqrt{3}q_2$ with small denominators, so $p_3-q_2q_3\sqrt{3}$ is small. Then $q_2q_3\sqrt{3}$ is close to the integer $p_3$, and if you chose the right meanings of "really" and "small," $q_2q_3\sqrt{2}$ is still close to the integer $p_2q_3$. I think this is typically far from efficient. | |
| May 12, 2015 at 20:11 | comment | added | wdlang | It is an equally difficult problem. Anyway, I want a general algorithm. | |
| May 12, 2015 at 19:52 | answer | added | Igor Rivin | timeline score: 11 | |
| May 12, 2015 at 19:30 | comment | added | Will Jagy | how do you do $$ \cos (t) + \cos (\sqrt{2} t) + \cos (\sqrt{3} t) > 3 - 10^{-9}? $$ | |
| May 12, 2015 at 19:06 | review | First posts | |||
| May 12, 2015 at 19:17 | |||||
| May 12, 2015 at 19:01 | history | asked | wdlang | CC BY-SA 3.0 |