Timeline for Natural topologies for the space of rational functions
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 29 at 1:23 | answer | added | Vladimir Pestov | timeline score: 1 | |
| Jul 20, 2015 at 7:53 | vote | accept | Arnold Neumaier | ||
| Jul 19, 2015 at 16:54 | comment | added | Joe Silverman | Okay, but since it's dealing with iteration, and the degree of $f^n$ is $(\deg f)^n$, somehow it needs to be relating maps of differing degrees. In any case, Laura would be a good person to ask about this. | |
| Jul 19, 2015 at 13:45 | comment | added | Arnold Neumaier | @JoeSilverman: As far as I could see, the paper works throughout with constant degree. | |
| Jul 19, 2015 at 13:37 | comment | added | Joe Silverman | Not sure if it's quite what you need, but there's a paper by Laura DeMarco, "Iteration at the boundary of the space of rational maps", Duke Math. Journal. 130 (2005) 169-197, that might be relevant. In any case, I seem to recall that she considers some sort of inductive (projective?) limit of the space of rational functions of degree $d$ over all $d$. The paper is available here: math.northwestern.edu/~demarco/Duke_boundary.pdf | |
| Jul 19, 2015 at 13:13 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
added restriction $a\ne0$
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| Jul 19, 2015 at 13:04 | history | edited | Arnold Neumaier | CC BY-SA 3.0 |
added details to the specification
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| Jul 19, 2015 at 12:55 | comment | added | Arnold Neumaier | I want a topology on the space of all rational functions of arbitrary denominator degree (and, if needed, a finite limit for $z\to\infty$) with properties that imply the above special cases. | |
| Jul 19, 2015 at 12:38 | comment | added | Joe Silverman | As long as you avoid letting $a\to0$, you can just take the distance from $a/(b-z)$ to $a'/(b'-z)$ to be $|b/a-b'/a'|$, I think. But if you want a nice metric topology that's okay for all $(a,b)\in\mathbb C^2$, there may well be a serious problem in the neighborhood the line $a=0$. | |
| Jul 19, 2015 at 12:30 | answer | added | Gerald Edgar | timeline score: 5 | |
| Jul 19, 2015 at 11:54 | answer | added | priel | timeline score: 7 | |
| Jul 19, 2015 at 11:48 | answer | added | Joe Silverman | timeline score: 2 | |
| Jul 19, 2015 at 11:24 | history | asked | Arnold Neumaier | CC BY-SA 3.0 |