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.