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

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.

preprint2013arXivOpen access
Sanjeeva BalasuriyaKathrin Padberg-Gehle
math.DS
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Sanjeeva BalasuriyaKathrin Padberg-Gehle

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