SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS

@article{Arguillre2015SUBRIEMANNIANSO,
  title={SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS},
  author={S. Arguill{\`e}re and E. Tr{\'e}lat},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2015},
  volume={16},
  pages={745 - 785}
}
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… Expand
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