Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds

Abstract

The paper deals with a quasiperiodically excited natural Lagrangian system on a Riemannian manifold. We find sufficient conditions under which this system has a weak Besicovitch quasiperiodic solution minimizing the averaged Lagrangian. It is proved that this solution is indeed a twice continuously differentiable uniformly quasiperiodic function, and the corresponding system in variations is exponentially dichotomous on the real axis.