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Pré-Publication, Document De Travail Année : 2016

Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics

Résumé

We study the variation of a smooth volume form along extremals of a variational problem with nonholonomic constraints and an action-like Lagrangian. We introduce a new invariant describing the interaction of the volume with the dynamics and we study its basic properties. We then show how this invariant, together with curvature-like invariants of the dynamics, appear in the expansion of the volume at regular points of the exponential map. This generalizes the well-known expansion of the Riemannian volume in terms of Ricci curvature to a wide class of geometric structures, including all sub-Riemannian manifolds.

Dates et versions

hal-01284352 , version 1 (07-03-2016)

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Andrei Agrachev, Davide Barilari, Paoli Elisa. Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics. 2016. ⟨hal-01284352⟩
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