Normally hyperbolic invariant manifolds potential

Figure 3.25(a) shows a case where a strong correlation exists between processes of crossing two neighboring barriers. This correlation results from direct intersection between the stable and unstable manifolds of the normally hyperbolic invariant manifolds located on the tops of neighboring barriers. Then, some of the orbits starting from one of the normally hyperbolic invariant manifolds directly reach the other one without falling into the potential well. Some other orbits may fall into the well and would take some time to reach the other manifold. The ratio of these two types of orbits depends on how steep the intersection is. 

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