Separatrix (dynamical systems)

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In mathematics, a separatrix refers to the boundary separating two modes of behaviour in a differential equation. For example, consider the differential equation describing the motion of a pendulum:

{d^2\theta\over dt^2}+{g\over l} \sin\theta=0.

The separatrix marks the transition between the pendulum swinging back and forth and the pendulum making full circles.

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