Hamiltonian System and Conjugate Gradient System (Hamiltonian, Potential, and Lyapunov Functions)

The system dx/dt = x^2 + 2x*y, dy/dt = 1 - 2x*y - y^2 is Hamiltonian. Why? What is the Hamiltonian function? How is the phase portrait related to the level curves of the Hamiltonian function? What is the conjugate gradient system and potential function? What is a Lyapunov function for the conjugate gradient system? amzn.to/35Wxabr. (Differential Equations, 4th Edition (by Blanchard, Devaney, and Hall))
#hamiltonian #gradient #lyapunov
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