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Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. (English) Zbl 1091.37018
The authors prove that the mechanical system consisting of a geodesic flow in a manifold plus a time quasi-periodic potential possesses orbits of unbounded energy, provided that the geodesic flow and the potential satisfy some mild nondegeneracy assumptions.

MSC:
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
53D25 Geodesic flows in symplectic geometry and contact geometry
70H08 Nearly integrable Hamiltonian systems, KAM theory
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