Lagrangian systems on hyperbolic manifolds

  title={Lagrangian systems on hyperbolic manifolds},
  author={Philip Boyland and Christopher Gol'e},
  journal={arXiv: Dynamical Systems},
This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincar\'e ball, Theorem A asserts that there are minimizers of the lift of the Lagrangian system that are a bounded distance away and have a variety of approximate speeds. Theorem B gives the existence of a collection of compact invariant sets of the Euler-Lagrange flow… 
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