Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds
AbstractThe 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.
How to Cite
ParasyukI. O. “Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 10, Oct. 2014, pp. 1387–1406, http://umj.imath.kiev.ua/index.php/umj/article/view/2230.