Author:
Arguillère Sylvain,Trélat Emmanuel
Abstract
In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide examples of normal and of abnormal geodesics in that infinite-dimensional context. The momentum formulation gives a sub-Riemannian version of the Euler–Arnol’d equation. Finally, we establish some approximate and exact reachability properties for diffeomorphisms, and we give some consequences for Moser theorems.
Publisher
Cambridge University Press (CUP)
Reference46 articles.
1. Controllability criterion for systems in a Banach space (generalization of Chow’s theorem);Dudnikov;Ukrain. Mat. Zh.,1980
2. On the existence and nonexistence of Lagrange multipliers in Banach spaces
3. Singular Trajectories of Control-Affine Systems
4. Diffeomorphism groups and pattern matching in image analysis;Trouvé;Int. J. Comput. Vis.,2005
5. Local Geometry of Deformable Templates
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Shape Spaces: From Geometry to Biological Plausibility;Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging;2023
2. Shape Spaces: From Geometry to Biological Plausibility;Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging;2022
3. Finite codimensional controllability and optimal control problems with endpoint state constraints;Journal de Mathématiques Pures et Appliquées;2020-06
4. A remark on vanishing geodesic distances in infinite dimensions;Proceedings of the American Mathematical Society;2020-03-04
5. Sub-Riemannian Methods in Shape Analysis;Handbook of Variational Methods for Nonlinear Geometric Data;2020