Techniques from dynamical systems, specifically from bifurcation theory, are used to investigate the occurrence of Skiba (or indifference) points in one state, one co-state control systems, for which the effect of the control has a definite direction. The parameter region for which Skiba points occur can be determined: it is bounded by heteroclinic bifurcation manifolds. Furthermore, a local criterion ensuring the existence of Skiba points in systems with small discount rates is developped. The analysis is applied to the shallow lake system investigated by Malar, Xepapapedas and de Zeeuw (2000). For this system, it is shown that for any given parameter value, there is at most one Skiba point.