The diameter of the symplectomorphism group is infinite

DOI10.1007/BF01239516zbMath0725.58006OpenAlexW2010219715MaRDI QIDQ2276815

Tudor S. Ratiu, Ya. M. Ehliashberg

Publication date: 1991

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143860

zbMATH Keywords

Riemannian manifoldgroups of diffeomorphismsvolume-preserving diffeomorphismssymplectic diffeomorphisms

Mathematics Subject Classification ID

Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20)

Related Items (14)

QUASI-MORPHISMS AND L^p-METRICS ON GROUPS OF VOLUME-PRESERVING DIFFEOMORPHISMS ⋮ Generalized fluid flows, their approximation and applications ⋮ Fredholm properties of Riemannian exponential maps on diffeomorphism groups ⋮ The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms ⋮ The \(L^p\)-diameter of the group of area-preserving diffeomorphisms of \(S^2\) ⋮ Geometric investigations of a vorticity model equation ⋮ A short proof that the \(L^p\)-diameter of \(\mathrm{Diff}_0(S,\mathrm{area})\) is infinite ⋮ Singularity formation in the incompressible Euler equation in finite and infinite time ⋮ Metric properties of the group of area preserving diffeomorphisms ⋮ Diffeomorphism groups of compact manifolds ⋮ Can we run to infinity? The diameter of the diffeomorphism group with respect to right-invariant Sobolev metrics ⋮ Geodesic distance for right-invariant metrics on diffeomorphism groups: critical Sobolev exponents ⋮ Topological lower bounds on the distance between area preserving diffeomorphisms ⋮ Various formulations and approximations of incompressible fluid motions in porous media

Cites Work

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• The Hamiltonian structure of the Maxwell-Vlasov equations
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Groups of diffeomorphisms and the motion of an incompressible fluid
• On the topological properties of symplectic maps
• Structure of the group of homeomorphisms preserving a good measure on a compact manifold

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