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SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS

  • Sylvain Arguillère (a1) and Emmanuel Trélat (a2)

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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SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS

  • Sylvain Arguillère (a1) and Emmanuel Trélat (a2)

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