13 pages, 6 figs.-- Physica D (in press).-- Digital.CSIC post-print version available: http://digital.csic.es/handle/10261/7507We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics appearing, which can be embedded in three dimensions. We perform a bi-orthogonal decomposition analyzing the minimum number of modes necessary to find the same organization of unstable orbits.Partial support from ANPCyT and UBACyT, Argentine agencies, is acknowledged. HSW thanks the MECyD, Spain, for an award within the Sabbatical Program for Visiting Professors, and to the Universitat de les Illes Balears for the kind hospitality extended to him.Peer reviewed