Repelling periodic trajectory

Although unstable, this periodic orbit is an example of classical motion which leaves the molecule bounded. Other periodic and nonperiodic trajectories of this kind may exist at higher energies. The set of all the trajectories of a given energy shell that do not lead to dissociation under either forwarder backward-time propagation is invariant under the classical flow. When all trajectories belonging to this invariant set are unstable, the set is called the repeller [19, 33, 35, 48]. There also exist trajectories that approach the repeller in the future but dissociate in the past, which form the stable manifolds of the repeller Reciprocally, the trajectories that approach the... 

Solution No. Trajectories are repelled to infinity, and never return. So infinity acts like an attracting fixed point. Chaotic behavior should be aperiodic, and that excludes fixed points as well as periodic behavior. ... 

Fig. 10.2.4. Saddle-node periodic orbits in (a) the cycle L is stable in the interior region and unstable in the exterior region. When hp < 0, it is attractive for the point inside it, and repelling for outer trajectories (b).

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