Separation Conditions for Iterated Function Systems with Overlaps on Riemannian Manifolds

We formulate the weak separation condition and finite type for conformal iterated function systems on Riemannian manifolds with nonnegative Ricci curvature, generalize main theorems by Lau et al. (Monatsch Math 156:325–355, 2009). also obtain a formula Hausdorff dimension of self-similar set defined an system satisfying condition, generalizing corresponding result Jin Yau (Commun Anal Geom 13:821–843, 2005) Ngai (Adv 208:647–671, 2007) Euclidean spaces. Moreover, we graph generated graph-directed extending (Nonlinearity 23:2333–2350, 2010).