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The aim of this talk is to show how the simple robust Guckenheimer and Holmes (GH) heteroclinic network occurring in 3-dimensional symmetric systems of ordinary differential equations can be lifted to more complicated robust heteroclinic networks in higher-dimensional systems. We pose the problem in the coupled cell network formalism, use a network lifting method and prove that flow invariant subspaces given by the network structure of the n-cell lifts are the main ingredient to show that the dynamics of each n-dimensional lift supports a more complicated heteroclinic network that includes the GH heteroclinic network as a subnetwork. This is a joint work with M. Aguiar (Porto) and H. Ruan (Hamburg).
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