Well-posed infinite horizon variational problems on a compact manifold



We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i.e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics.


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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.SISSA/ISASTriesteItaly
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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