Attractor and spatial chaos for the Brusselator in RN

Moreover we give a more detailed study of spatial chaos of the attractor A for the Brusselator in RN. We interpret a group of spatial shifts as a dynamical system which acts on the attractor A. By using the technique of unstable manifolds, it is proved that this dynamical system is chaotic. In order to clarify the nature of this chaos, we construct the Lipschitz-continuous homeomorphic embedding of a typical model dynamical system whose chaotic behavior is evident, into the spatial shifts on the attractor A. This typical dynamical system generalizes the symbolic system. It was first introduced by Zelik.