and the unstable space 
, are determined by the eigenvectors
of 
. The stable direction is calculated from
Solving this system of simultaneous equations for 
and 
gives the unnormalized eigenvector for the unstable space as
Similarly, the stable space is found from the eigenvalue equation
for 
:
Solving this set of simultaneous equations shows that the stable space is just the z-axis,
In fact, the z-axis is invariant for the whole flow (i.e., if z = 0 then
for all t) so the z-axis is the global stable manifold at a,
.