von Neumann Map applied to von Neumann Quadratic Equation \(a x^2 + bx+c=0\: \:(a \neq 0)\)
hassolutions \[
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \]
Now The Lorenz Equations:
\[\begin{array}{rcl}
\dot{x} & = & \sigma(y-x) \\
\dot{y} & = & \rho x - y - xz \\
\dot{z} & = & -\beta z + xy
\end{array}
\] Test ok!
COMMENTS: Use Double-Dollar Signs for Displaymode... Use Slash-Parentheses for
in-line Math mode. Don't use single-dollar signs.
When $a \ne 0$, \(a \ne 0\) there are two solutions to \(ax^2 + bx + c = 0\) and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
