Timeline for structural stability
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 14, 2011 at 10:53 | comment | added | ivo | Benoit, map f is from R to R | |
| Mar 14, 2011 at 9:09 | comment | added | Benoît Kloeckner | Ivo, the domain and range of your map is not clear, and you should give motivation and context to your question. | |
| Mar 13, 2011 at 20:51 | answer | added | passerby | timeline score: -1 | |
| Mar 13, 2011 at 12:43 | comment | added | ivo | Niyazi, if a is between 0 and 1 then our f has only one fixed point right? If I make a small perturbation of f this map has also one fixed point, because the derivation of map x-f(x)-c is always greater than zero, this map will be increasing and therefore we will have only one zero | |
| Mar 13, 2011 at 12:35 | comment | added | Niyazi | ivo, it was just an example. use $c/2.$ you just need to shift graphs by $c/2$ then the C^r distance between new function and the old one will be small. The number of fixed points is not preserved. It will show that whatever c>0 is given, one can construct a new close function which is not top. conjugate with the original function. | |
| Mar 13, 2011 at 10:12 | comment | added | ivo | Niyazi, to prove that f is not structurally stable I need to construct for every c>0 function g such that C^r distance between f and g is less than c and such that there is no top. conjugacy between f and g. In your answer you constructed such function for c=0.3183. This is not enough | |
| Mar 13, 2011 at 4:18 | comment | added | Niyazi | ivo, when a\in (0,1), consider h=asin(x)+0.3183. Then compare the fixed points. I can't see why this question is hard to solve | |
| Mar 13, 2011 at 0:31 | history | asked | ivo | CC BY-SA 2.5 |