00894nas a2200109   4500008004100000245007500041210006900116260001000185520052800195100002500723856003600748       2010                        en  d00aWell-posed infinite horizon variational problems on a compact manifold0 aWellposed infinite horizon variational problems on a compact man  bSISSA3 aWe 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 dynamics1 aAgrachev, Andrei, A.  uhttp://hdl.handle.net/1963/6458