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Results tagged with sg.symplectic-geometry
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user 56878
Hamiltonian systems, symplectic flows, classical integrable systems
3
votes
1
answer
506
views
When is the gradient of a Hamiltonian function a Liouville vector field?
Let $(M, \omega)$ be a symplectic manifold, $H$ a Hamiltonian function on $M$, $Y = H^{-1}(c)$ for a regular value $c$, and $J$ a compatible almost complex structure.
If $X_H$ is the Hamiltonian vect …
- 3,058
24
votes
1
answer
2k
views
Why are Lagrangian submanifolds called Lagrangian?
Much of the terminology in symplectic geometry comes from classical mechanics: the symplectic manifold is modeled on a cotangent bundle $T^*N$ of some configuration space $N$ with local position coord …
- 3,058