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Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    I. O. Parasyuk

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  1. I. O. Parasyuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 10, pp. 1387–1406, October, 2014.

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Parasyuk, I.O. Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds. Ukr Math J 66, 1553–1574 (2015). https://doi.org/10.1007/s11253-015-1031-2

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  • DOI: https://doi.org/10.1007/s11253-015-1031-2

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