%0 Journal Article %J Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 %D 2010 %T Well-posed infinite horizon variational problems on a compact manifold %A Andrei A. Agrachev %X 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 %B Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 %I SISSA %G en %U http://hdl.handle.net/1963/6458 %1 6404 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:50:56Z\\nNo. of bitstreams: 1\\ndiscount.pdf: 256111 bytes, checksum: 78c64c5edffbe71a9201c6023252b87d (MD5) %R 10.1134/S0081543810010037