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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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Wrzlprmft
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user1942348
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1 Answers1

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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.

Futurologist
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  • A homoclinic trajectory is traversed in infinite time – At a first glance this is not correct. You could have a trajectory starting and ending at a Norton dome which is traversed in finite time. – Wrzlprmft Jun 17 '19 at 06:24
  • @Wrzlprmft If a system has smooth right hand side, reaching equilibrium in finite time violates uniqueness and existence theorem. – Evgeny Jun 17 '19 at 09:36