3Hamiltonian vector fields

III Symplectic Geometry



3 Hamiltonian vector fields
Symplectic geometry was first studied by physicists, who modeled their systems
by a symplectic manifold. The Hamiltonian function
H C
(
M
), which returns
the energy of a particular configuration, generates a vector field on
M
which is
the equation of motion of the system. In this chapter, we will discuss how this
process works, and further study what happens when we have families of such
Hamiltonian functions, giving rise to Lie group actions.

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