Timeline for Topology of the Yoccoz puzzles at depth-$n$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2019 at 10:52 | comment | added | Yee Neil | OK, thanks for your comments. | |
| Sep 26, 2019 at 16:00 | comment | added | Lasse Rempe | Yes, this is a masterful account of the Yoccoz puzzle by Milnor; it is the paper where I first learned about these techniques. You will learn much by studying it carefully. | |
| Sep 25, 2019 at 2:39 | comment | added | Yee Neil | Ok, I got it, thanks,Professor! I am reading one paper titled "Periodic Orbits Externals Rays and the Mandelbrot Set An Expository Account" by Milnor recently .Do you think that I can get more details in this paper about this question! | |
| Sep 17, 2019 at 11:30 | comment | added | Lasse Rempe | In terms of how complicated it is, it is not that complicated if you know where the parameter is. Of course, the number of rays involved in the puzzle does grow exponentially with the level of the pieces. | |
| Sep 17, 2019 at 11:29 | comment | added | Lasse Rempe | You need to know where your parameter is in the Mandelbrot set. One way to describe this is with an external angle. This is the angle of a parameter ray which, a posteriori, we know must land at the parameter. But it can also be described combinatorially, e.g. as an angle whose parameter ray is not separated from the given parameter by pairs of periodic or pre-periodic rays landing together. See Schleicher's paper on fibers of the Mandelbrot set, for example. | |
| Sep 14, 2019 at 8:56 | comment | added | Yee Neil | Does it mean that we need to know how each preimage of those external rays and themselves maps to another one? If that is right, I think it must be very complicated to determine higher levels even we know that is determined by the initial state of the puzzle. | |
| Sep 13, 2019 at 9:33 | history | answered | Lasse Rempe | CC BY-SA 4.0 |