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toastermm
toastermm is offline
#2
Jun15-12, 04:17 PM
P: 3
Continuing to the Jacobian anyways, we arrive at

[itex]
J = \left[
\begin{array}{ccc}
-1 - (\bar{Y} + \bar{Z}) & -\bar{X} & -\bar{X} \\
a\bar{Y} & a\bar{X}-1 & 0 \\
a\bar{Z} & 0 & a\bar{X}-1
\end{array}
\right].
[/itex]

Plugging in what we know,

[itex]
J = \left[
\begin{array}{ccc}
-a & -\frac{1}{a} &-\frac{1}{a} \\
a\bar{Y} & 0 & 0 \\
a\bar{Z} & 0 & 0
\end{array}
\right].
[/itex]

This means that the trace of the Jacobian is negative, i.e. [itex] tr(J) = -a < 0 [/itex]. Also that the determinant is equal to zero. My book does not talk about what happens when the determinant of the Jacobian is zero. Any insights?