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We study Hamiltonian systems which generate extremal flows of regular
variational problems on smooth manifolds and demonstrate that
negativity of the generalized curvature of such a system implies
the existence of a global smooth optimal synthesis for the infinite
horizon problem.
We also show that in the Euclidean case negativity of the generalized curvature is a consequence of
the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for...
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