Gromov hyperbolic graphs arising from iterations

For a contractive iterated function system (IFS), it is known that there natural hyperbolic graph structure (augmented tree) on the symbolic space of IFS reflects relationship among neighboring cells, and its boundary with Gromov metric Hölder equivalent to attractor K [14], [26], [28]. This setup was taken up study probabilistic potential theory [21], [20], bi-Lipschitz equivalence [29]. In this paper, we formulate broad class graphs, called expansive capture most essential properties from augmented trees boundaries (e.g., special geodesics, bounded degree property, doubling equivalence). We also new “weighted” investigate connection self-similar energy form in analysis fractals.