Hamiltonian Flow Maps are Symplectic

As we saw at the end of the last chapter, the variational equations describe the change in an infinitesimal perturbation of a solution of a dynamical system. For the Hamiltonian system z = JVf/(z), these take the form  

This means that W JW is a constant matrix. Observe that W(f) = )) and 

This proves that the flow map of a Hamiltonian system is a symplectic map. 

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