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1 LJLL - Laboratoire Jacques-Louis Lions

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.

Keywords : sub-Riemannian geometry in infinite dimension group of diffeomorphims





Author: Sylvain Arguillere - Emmanuel Trélat -

Source: https://hal.archives-ouvertes.fr/



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