Entropy and complexity of a path in sub-Riemannian geometry
Frédéric Jean (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset of a metric space is the minimum number of balls of a given radius needed to cover . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an -neighborhood of...