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Required fields*

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  • $\begingroup$ On a sphere or on a cylinder? $\endgroup$ Commented Dec 14, 2021 at 22:57
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    $\begingroup$ What do x and y represent? To draw a phase portrait on a sphere you need a vector field (or ODE) on a sphere. In the cylinder example, the field/ODE is invariant under the transformation $x \mapsto x+2\pi$, which allows one to map the vector field $(\dot x, \dot y) = (y, -\sin x)$ on the plane to a vector field on a cylinder. There's no such natural mapping onto the sphere, so you would have to define one. $\endgroup$ Commented Dec 15, 2021 at 3:04