| Abstract: | At the beginning of investigations in spatially homogeneous branching processes in Euclidean space (Liemant 1]) it seemed to be obvious that the existence of equilibria implies criticality of branching. This prejudice was disproved by the example 2] of a subcritical homogeneous branching equilibrium in dimension one. We prove that supercritical homogeneous branching processes in Euclidean space and, more general, in a broad class of topological groups have no (non – void, homogeneous) equilibria. |
