Timeline for Proven chaos in logistic maps
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2022 at 21:20 | history | edited | bobuhito | CC BY-SA 4.0 |
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| Feb 4, 2022 at 22:21 | comment | added | coudy | @Romik Let me phrase it as follows: there is a large set of parameters for which the dynamics is reasonably well-understood but checking if a given computable number, say a rational, belongs to that set may be very hard. | |
| Feb 4, 2022 at 22:15 | comment | added | coudy | @Romik The monotonicity of the topological entropy (and its continuity) is due to Adrien Douady, circa 1995. It relies on the work of Milnor and Thurston from 1988 that describes the dynamics of interval maps in terms of kneading invariants. See Vaughn Climenhaga's answer for additional references. | |
| Feb 4, 2022 at 9:38 | comment | added | Dan Romik | @coudy the “answer” to some sufficiently modified version of OP’s question may be known (and that’s quite interesting to hear). But in your answer you yourself seem to admit that for particular values of $r$ and $x$ the answer is likely not known, nor obtainable using known methods — is that a correct interpretation of what you wrote? And could you give a reference to the result about values of $r$ larger than 3.5699…? | |
| Feb 3, 2022 at 14:18 | history | became hot network question | |||
| Feb 3, 2022 at 13:06 | answer | added | Vaughn Climenhaga | timeline score: 7 | |
| Feb 3, 2022 at 12:58 | comment | added | coudy | @Romik the answer is known for far many more parameters than $r=4$. Symbolic dynamics for interval maps has been thoroughly studied. | |
| Feb 3, 2022 at 12:53 | answer | added | coudy | timeline score: 8 | |
| Feb 3, 2022 at 9:25 | history | edited | YCor |
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| Feb 3, 2022 at 8:33 | comment | added | Dan Romik | See a related discussion here. It appears that the answer is not known except for $r=4$. | |
| Feb 3, 2022 at 7:28 | answer | added | LeechLattice | timeline score: 8 | |
| Feb 3, 2022 at 6:17 | history | asked | bobuhito | CC BY-SA 4.0 |