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

作者：Li Chengbo^*

来源：Acta Applicandae Mathematicae, 2012, 117(1): 71-91.

DOI：10.1007/s10440-011-9650-6

• Hyperbolic flows
• Sub-Riemannian structures
• Anosov flows
• Curves in Lagrange Grassmannians
• Curvature maps
• Magnetic field on Riemannian manifolds with transverse symmetries

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.

• 出版日期2012-2
• 单位天津大学