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Abstract: We give an effective sufficient condition for a variational problem withinfinite horizon on a compact Riemannian manifold M to admit a smooth optimalsynthesis, i. e. a smooth dynamical system on M whose positivesemi-trajectories are solutions to the problem. To realize the synthesis weconstruct a well-projected to M invariant Lagrange submanifold of theextremals- flow in the cotangent bundle T*M. The construction uses thecurvature of the flow in the cotangent bundle and some ideas of hyperbolicdynamics.



Author: Andrei Agrachev

Source: https://arxiv.org/







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