Plane Couette -

Upper branch unstable manifold

	blue: The unstable manifold (S-symmetric subspace) of the UB equilibrium traced out by a set of trajectories initialized along one of the pair of complex-eigenvalue eigenvectors. black: A single UB unstable manifold trajectory traced through a trubulent episode to the decay to the laminar state LM. [L_x, L_y, L_z] = [5.51, 2, 2.51] cell, Re=400. For this cell every initial condition appears to eventually decay to the laminar solution LM, upper left corner. The dots are equidistant in time: a slowdown that signals proximity to an equilibrium is evident in the neighborhoods of the UB and LM equilibria.

Clearly, the eigenvectors of an equilibrium offer a natural low-dimensional basis for visualization of the dynamics in its neighborhood. But how do we put these together into a global visualization of the dynamics?