Moreover, the x-axis is the unstable subspace for the linearized vector field and the y axis is the stable subspace for the linearized vector field. The global unstable manifold of the origin is the s...Moreover, the x-axis is the unstable subspace for the linearized vector field and the y axis is the stable subspace for the linearized vector field. The global unstable manifold of the origin is the set of initial conditions having the property that the trajectories through these initial conditions approach the origin at an exponential rate as t \rightarrow -\infty.
