Geodesic equations on diffeomorphism groups.
Geodesics in the compactly supported Hamiltonian diffeomorphism group.
Geometry on the group of Hamiltonian diffeomorphisms.
Groupe des difféomorphismes et espace de Teichmüller d'une surface
Groupes d’automorphismes de et équations différentielles
Groups of diffeomorphisms and Lie theory.
Hofer’s metrics and boundary depth
We show that if is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of Hamiltonian diffeomorphisms of has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer’s metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in when satisfies...
Homeotopy groups of punctured spheres with holes
Homotopie des espaces de concordances
Homotopy type of automorphism groups of manifolds
Invariants analytiques des champs de vecteurs de
On démontre qu’il ne peut exister de système complet d’invariants analytiques pour l’action du groupe des germes des difféomorphismes sur les champs de vecteurs pour un champ dont la forme normale a un champ réduit associé nul.
Ito equation as a geodesic flow on
The Ito equation is shown to be a geodesic flow of metric on the semidirect product space , where is the group of orientation preserving Sobolev diffeomorphisms of the circle. We also study a geodesic flow of a metric.
Lie algebras connected with associative ones
Lie group structures on groups of diffeomorphisms and applications to CR manifolds
We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.
Local density of diffeomorphisms with large centralizers
Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Local Groups of Differentiable Transformations.
Local homology of groups of volume preserving diffeomorphisms. I
Local homology of groups of volume-preserving diffeomorphisms, II.
Local homology of groups of volume-preserving diffeomorphisms. III
Locally flat embeddings of Hilbert cubes are flat