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A Note on Hyperbolic Flows in Sub-Riemannian Structures with Transverse Symmetries

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Abstract

The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrangian distribution) on a symplectic manifold. We consider the Hamiltonian flows of the curve of least action of natural mechanical systems in sub-Riemannian structures with symmetries. We give sufficient conditions for the reduced flows (after reduction of the first integrals induced from the symmetries) to be hyperbolic in terms of the reduced curvature and show new examples of Anosov flows.

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  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, P.R. China

    Chengbo Li

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  1. Chengbo Li
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Correspondence to Chengbo Li.

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Li, C. A Note on Hyperbolic Flows in Sub-Riemannian Structures with Transverse Symmetries. Acta Appl Math 117, 71–91 (2012). https://doi.org/10.1007/s10440-011-9650-6

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  • DOI: https://doi.org/10.1007/s10440-011-9650-6

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