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Published online by Cambridge University Press: 28 October 2019
We introduce the Jacobi curve associated with a normalextremal. Heuristically, we would like to extractgeometric properties of the sub-Riemannian structureby studying the symplectic invariants of itsgeodesic flow. The simplest idea is to look forinvariants in its linearization. This subject isnaturally related to geodesic variations andgeneralizes the notion of Jacobi fields inRiemannian geometry to more general geometricstructures.
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