Timeline for Properties of a certain sequence
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2020 at 20:15 | comment | added | Jeremy Rouse | I would guess that the sequence $(x_{k})_{k}$ fails to be dense for an measure zero subset of $\lambda$'s that one could choose, so the generic case is presumably what you found in your numerical experiments. I don't know about your claim 2, my intuition would be that it is true. | |
| Nov 11, 2020 at 8:52 | vote | accept | Luka Thaler | ||
| Nov 11, 2020 at 8:52 | comment | added | Luka Thaler | Jeremy thank you for your answer. This was quite unexpected! Do you think that similar convergence (maybe to some other value on the interval) also happens for generic irrational $\lambda$ (or perhaps for Diophantine numbers). Can they be somehow roughly characterized? I also hope that my second claim is wrong, meaning that for generic rational number one would get periodic sequence. | |
| Nov 10, 2020 at 22:13 | history | answered | Jeremy Rouse | CC BY-SA 4.0 |