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Results tagged with sg.symplectic-geometry
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user 5740
Hamiltonian systems, symplectic flows, classical integrable systems
30
votes
Accepted
Classical mechanics motivation for poisson manifolds?
For many reasons and purposes, it is the Poisson bracket, not the symplectic form, that plays a primary role.
Equations of motion and, more generally, the evolution of observables have an easy fo …
- 14.5k
14
votes
Accepted
Which tensor fields on a symplectic manifold are invariant under all Hamiltonian vector fields?
Any symplectic linear transformations in $T_xM$ is locally realizable as a Hamiltonian vector field, thus for questions 1 and 2, one can profitably use representation theory of the symplectic group.
…
- 14.5k
28
votes
Accepted
Book on symplectic geometry
If you are physically inclined, V.I.Arnold's Mathematical methods of classical mechanics provides a masterful short introduction to symplectic geometry, followed by a wealth of its applications to cla …
- 14.5k
12
votes
Intuition for symplectic groups
This is an outgrowth of an extended comment dealing with the superficial difference between symplectic and orthogonal rotations embedded in the question. I posit that the theory for symplectic groups …
- 14.5k