Timeline for Necessary Conditons For Implicit Function
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jun 28, 2011 at 16:36 | comment | added | Pietro Majer | Yes: e.g. for $f:\Lambda \times X\to Y$, I mean non-uniqueness, for a given $\lambda\in\Lambda $, of a point $x$ such that $f(\lambda,x)=0$. If this happens in any nbd of some $\lambda_0$, we say $\lambda_0$ is bifurcation point for the equation $f(\lambda,x)=0$. I meant to recall that a relevant case (thus not a pathology but an important phenomenon) where the picture of the IFT does not hold is this, bifurcation. | |
| Jun 25, 2011 at 11:58 | comment | added | Willie Wong | @Pietro: I'm sorry, I don't quite follow. In the context, what is non-unique? Just to see if I understand correctly, are you referring to the case where the implicit relation is multi-valued (for example the relation from $x$ to $y$ near $(1,0)$ for the function $f(x,y) = x^2 + y^2 = 1$)? Thanks. | |
| Jun 25, 2011 at 5:33 | history | answered | Pietro Majer | CC BY-SA 3.0 |