Timeline for Fixed points of a function $z\mapsto\overline{P(z)}$ of a complex variable
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2022 at 1:40 | vote | accept | user159888 | ||
| Feb 15, 2022 at 13:53 | answer | added | Alexandre Eremenko | timeline score: 8 | |
| Feb 15, 2022 at 13:24 | comment | added | YCor | An obvious remark (certainly known to the OP but possibly useful for readers). These are the fixed points of $Q(z)=\overline{P(z)}$. Then $Q\circ Q=\bar{P}\circ P$, which is a polynomial of degree $n^2$. So if $n>1$, every fixed point is a zero of $(\bar{P}\circ P)(t)-t$, so the set of fixed points is finite and bounded above by $n^2$. | |
| Feb 15, 2022 at 13:23 | comment | added | user159888 | Great. Now it is more clear. Thanks | |
| Feb 15, 2022 at 13:17 | history | edited | YCor | CC BY-SA 4.0 |
clarified title
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| Feb 15, 2022 at 9:55 | history | edited | user159888 | CC BY-SA 4.0 |
added 2 characters in body
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| Feb 15, 2022 at 6:38 | comment | added | user159888 | Thanks. Will look at it. Yes | |
| Feb 15, 2022 at 6:16 | comment | added | Vik78 | This paper seems to address the question, and the upper bound indeed appears to be $3n - 2$. I didn’t read it in detail though. I assume you meant to require $n > 1$. ams.org/journals/proc/2003-131-02/S0002-9939-02-06476-6/… | |
| Feb 15, 2022 at 6:09 | comment | added | abx | $z=\overline{z}$ has more than 2 solutions... | |
| Feb 15, 2022 at 4:35 | history | asked | user159888 | CC BY-SA 4.0 |