- #1

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## Homework Statement

For the system:

[tex]

\frac{dx}{dt}=x\cos{xy}

\: \:

\frac{dy}{dt}=-y\cos{xy}[/tex]

(a) is Hamiltonian with the function:

[tex]

H(x,y)=\sin{xy}[/tex]

(b) Sketch the level sets of H, and

(c) sketch the phase portrait of the system. Include a description of all equilibrium points and any saddle connections.

## Homework Equations

## The Attempt at a Solution

[tex]\frac{\partial H}{\partial y}=y\cos{xy}=-g \\

\frac{\partial H}{\partial x}=x\cos{xy}=f[/tex]

So the function is Hamiltonian. I see that the equilibrium points are (0,0) and (±√π/2,±√π/2) by inspection. The problem I have is that the second set of equilibria have complex roots, but I don't see any of that behavior when I graph the phase portrait with pplane.