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Abstract: The curvature and the reduced curvature are basic differential invariants ofthe pair Hamiltonian system, Lagrange distribution on the symplecticmanifold. It is shown that the negativity of the reduced curvature implies thehyperbolicity of any compact invariant set of the Hamiltonian flow restrictedto a prescribed energy level. We consider the Hamiltonian flows of the curve ofleast action of natural mechanical systems in sub-Riemannian structures withsymmetries. We give sufficient conditions for the reduced flows afterreduction of the first integrals induced from the symmetries to be hyperbolicand show new examples of Anosov flows.



Author: Chengbo Li

Source: https://arxiv.org/



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