We study the variation of a smooth volume form along extremal s of a variational problem with nonholonomic constraints and an action-like L agrangian. 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 c urvature-like invariants of the dynamics introduced in , appear in the expansion of the vo lume at regular points of the exponential map. This generalizes the well-known expansio n of the Riemannian volume in terms of Ricci curvature to a wide class of geometric structures, i ncluding all sub-Riemannian manifolds.
|Titolo:||Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics|
|Autori:||Agrachev, A.; Barilari, D.; Paoli, E.|
|Data di pubblicazione:||Being printed|
|Appare nelle tipologie:||1.1 Journal article|