Timeline for If you perturb a polynomial by a smooth function, then is the signed number of small zeros of the perturbed equation the same as the lowest non zero derivative?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 15, 2013 at 6:01 | vote | accept | Ritwik | ||
| Jan 14, 2013 at 21:29 | comment | added | Alexandre Eremenko | In general, topological degree is explained in Milnor's book Topology from differentiable viewpoint, but perhaps there is no exact statement of Rouche's thm there. When I used a similar fact in my own paper, I refered to MR1789408 M. Cristea, A generalization of the argument principle, Complex Variables Theory Appl. 42 (2000), no. 4, 333–345. | |
| Jan 14, 2013 at 15:10 | comment | added | Ritwik | Thank you, that is exactly what I want to count. Is there a reference for this fact (that Rouche's theorem is valid for smooth functions)? | |
| Jan 14, 2013 at 15:06 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |