Fredholm properties of the \(L^2\) exponential map on the symplectomorphism group
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Publication:254834
DOI10.3934/jgm.2016.8.1zbMath1386.35318OpenAlexW2524229564MaRDI QIDQ254834
Publication date: 16 March 2016
Published in: Journal of Geometric Mechanics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/jgm.2016.8.1
PDEs in connection with optics and electromagnetic theory (35Q60) Statistical mechanics of plasmas (82D10) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Euler-Poisson-Darboux equations (35Q05) Calculus on manifolds; nonlinear operators (58C99) Nonlinear operators and their properties (47H99) Vlasov equations (35Q83)
Related Items
The coadjoint operator, conjugate points, and the stability of ideal fluids ⋮ Sobolev \(H^1\) geometry of the symplectomorphism group
Cites Work
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- Geodesics on the symplectomorphism group
- Infinite-dimensional Lie groups and algebras in mathematical physics
- On a non-linear equation related to the geometry of the diffeomorphism group
- On the volumorphism group, the first conjugate point is always the hardest
- Partial differential equations. I: Basic theory
- The Hamiltonian structure of the Maxwell-Vlasov equations
- The differentiable structure of three remarkable diffeomorphism groups
- Generalized fluid flows, their approximation and applications
- Topological methods in hydrodynamics
- For ideal fluids, Eulerian and Lagrangian instabilities are equivalent
- A biinvariant metric on the group of symplectic diffeomorphisms and the equation \((\partial/\partial t)\Delta F = \{\Delta F,F\}\)
- Conjugate points on geodesics of Hofer's metric
- Geodesic Vlasov equations and their integrable moment closures
- Singularities of the exponential map on the volume-preserving diffeomorphism group
- Groups of diffeomorphisms and the motion of an incompressible fluid
- Fredholm properties of Riemannian exponential maps on diffeomorphism groups
- Conjugate points in $\mathcal {D}_{\mu }(T^2)$
- An Infinite Dimensional Version of Sard's Theorem