Timeline for Variation of the argument of a rational function along a circle
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Oct 10, 2014 at 12:41 | vote | accept | Loïc Teyssier | ||
| Jul 11, 2014 at 10:02 | comment | added | Ali Taghavi | I think the question is interesting because it assigne a new quantity to a simple closed curve and a vec. field along it.the quantity is the length of interval image of $g$. As a possible another quantity could be "the total variation" of $g$. | |
| Jul 11, 2014 at 9:19 | comment | added | Loïc Teyssier | @AliTaghavi I'm not so sure it is such a great question actually. I was aware that if $C$ is spiralling enough then you can get large variations (that's why the question is asked for circles). But you're surely right that there should exists a bound in terms of the length (or more likely «curvature deviation») of $C$. | |
| Jul 11, 2014 at 9:03 | comment | added | Ali Taghavi | very nice question. I think the answer depend on the shape of $C$.For example put $f(z)=z$. Now let $C:[0,1]\to \mathbb{C}$ is a simple closed curve surrounding the origin which image of its restriction to $[0,1/2]$ is identical to the image of the spiral curve $\lambda(s)=e^{-s+is}$, for $s$ sufficiently large. for such curve the image of $g$ is large. So is it a good Idea that we expect to bound the length of $g$ in term of length of $C$? | |
| Jul 10, 2014 at 16:55 | answer | added | Robert Israel | timeline score: 2 | |
| Jul 10, 2014 at 15:53 | history | asked | Loïc Teyssier | CC BY-SA 3.0 |