Ehresmann Connection in the Geometry of Nonholonomic Systems
Entropy and complexity of a path in sub-riemannian geometry
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 the path,...
Entropy and complexity of a path in sub-Riemannian geometry
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 A of a metric space is the minimum number of balls of a given radius ε needed to cover A. 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 ε-neighborhood of the path,...