Period of a Homoclinic orbit

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A homoclinic orbit is a trajectory of a flow of a dynamical system which joins a saddle equilibrium point to itself.

What will be the period of Homoclinic orbit. Is it 2?

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1 Answer

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I think a homoclinic orbit is not a periodic orbit. For that reason it deosn't have a period. A homoclinic trajectory is traversed in infinite time. If you have a continuous family of periodic orbits inside the homoclinic one on your picture, then as the periodic orbits get closer to the homoclinic orbit, their period grows until it reaches infinity.

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