@article {2010,
title = {Well-posed infinite horizon variational problems on a compact manifold},
journal = {Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31},
number = {arXiv:0906.4433;},
year = {2010},
publisher = {SISSA},
abstract = {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},
doi = {10.1134/S0081543810010037},
url = {http://hdl.handle.net/1963/6458},
author = {Andrei A. Agrachev}
}