Article | REF: AF106 V1

Syst

Authors: Denis BONHEURE, Michel WILLEM

Publication date: October 10, 2008

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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 :

V(t,x)=
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Multi-boss solutions and chaotic dynamics