Ehresmann Connection in the Geometry of Nonholonomic Systems
Page 1
Displaying 1 – 3 of 3
Entropy and complexity of a path in sub-riemannian geometry
Frédéric Jean (2003)
ESAIM: Control, Optimisation and Calculus of Variations
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
Frédéric Jean (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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,...
Currently displaying 1 – 3 of 3
Page 1