Homoclinic orbit is defined as the intersection of stable and unstable manifold. In 2d case, dimension of both of 1 and they intersect at equilibrium point, so how can we have homoclinic orbit
2026-03-31 14:31:11.1774967471
The homoclinic orbit in the plane
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They may intersect tangent to each other. Think of an equilibrium point and connect it with itself with a single orbit, this single orbit is a homoclinic orbit and is part of the stable and the unstable manifold.