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Hamiltonian systems, symplectic flows, classical integrable systems
1
vote
Homogeneous symplectic manifolds
Some elements in the paper of Gery de Saxcé and Claude Vallée:
Construction of a central extension of a Lie group from its class of symplectic cohomology
https://www.sciencedirect.com/science/article/ …
1
vote
Geometric invariants of a Riemannian manifold encoded in certain moment map
Yes, all has been solved by Jean-Marie Souriau: see Barbaresco, F.; Gay-Balmaz, F. Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on S …