6. Multi-boss solutions and chaotic dynamics
The results we presented in the previous two paragraphs establish the existence of at least one homoclinic or heteroclinic solution of a given Hamiltonian system. In this paragraph, we consider multiplicity results. Moreover, the existence of a large number of homoclinic and heteroclinic orbits is frequently indicative of chaotic dynamics.
6.1 Homoclines and multi-boss heteroclines
The following theorems illustrate the kind of results we know about the multiplicity of solutions. Consider the potential :
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