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We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate...
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