Nonautonomous control of stable and unstable manifolds in two-dimensional flows

• Establishes theory to make stable/unstable manifolds move as specified by user.
• General nonautonomously perturbed movement is achievable in 2D flows.
• Rigorous error estimates are derived.
• Results are numerically verified.
• First study on controlling stable and unstable manifolds.

We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are to be moved to a user-specified time-varying location which is near the steady location. We determine the nonautonomous perturbation to the vector field required to achieve this control, and give a theoretical bound for the error in the manifolds resulting from applying this control. The efficacy of the control strategy is illustrated via a numerical example.