Heterocilinic Cycles

* Türkçesi için

The Heterocilinic cycle term is just inspired from mathematicly similarity of Heterocilinic orbit definition. In mathematics, a heterocilinic orbit is a trajectory of a flow of a dynamical system which joins two different equilibrium points. More precisely, a heteroclinic orbit lies in the intersection between the stable manifold of one equilibrium point and the unstable manifold of another equilibrium point. Maybe not literally, but, quite similar with this definition, some trajectories in CR3BP also make a flow (or cycles) which joins two different equilibrium points. Such the below plots show some heteroclinic cycle and connections with determining them poincare map. In fact, Heterocilinic Cycles are a connection between two periodic orbits around two different equilibrium point. But if a trajectory makes one or half turn around a equilibrum point, the  goes to another equilibrum and maked another  one or half turn, and repeat agaib and agian, then this may be called quasi-Heterocilinic Cycles.

Also if they joins only one equilibrium point, then they are called Homoclinic Cycles. These cycles can be very promising and adventageous for various science orbits.

To find these Heterocilinic Cycles, a simple Poincaré section between Invariant manifold tubes in neck region is taken;

Left side of upper figure show the manifold tubes, and their Poincaré section is in the right side. Black dotes are present Heterocilinic Cycles, which are shown in below;

Some other examples (Trajectories were found using Poincaré Section in intersection of two invariant manifold tubes, as similar as above);

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