Timeline for Decidability of 3 body problem
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2021 at 17:08 | comment | added | Peter Gerdes | That's a very good point about Q. It hadn't occured to me when first reading it but the way Smith's argument works requires finding initial conditions by continually refining some starting conditions to ensure each of infinietly many interactions comes out in the correct way. Smith shows that this process is effective so we can get computable reals as parameters which give rise to this problem but no guarantee it's possible in Q. | |
| Oct 17, 2021 at 22:54 | comment | added | Timothy Chow | I'm not sure either of these references addresses the stated question. Smith's paper leans heavily on uncountability, but the OP specifies rational initial positions and velocities. Hainry refers to reference [13] for details of the undecidability results, but [13] focuses on analytic functions, which again does not seem to match the OP's setup. | |
| Oct 16, 2021 at 15:15 | comment | added | Peter Gerdes | Ok, that's a good answer for 2 and 3 but I was vaguely aware that that passing close together was an issue and question 1 was designed specifically to deal with that objection as this kind of problem requires arbitrarily close approaches to generate the simulation problem. So I'm still curious about that answer. | |
| Oct 16, 2021 at 14:54 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |