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SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS
Published online by Cambridge University Press: 10 August 2015
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.
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- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 4 , September 2017 , pp. 745 - 785
- Copyright
- © Cambridge University Press 2015
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