Self-similar sets as hyperbolic boundaries Ka-Sing LauXiang-Yang Wang 28A7828A80boundarygeodesic rayhyperbolic graphiterated function systemself-similar setsopen set condition We show that, for an iterated function system $\{S_j\}_{j=1}^N$ of similitudes that satisfies the open set condition, there is a natural graph structure in the representing symbolic space to make it a hyperbolic graph, and the hyperbolic boundary is homeomorphic to the self-similar set generated by $\{S_j\}_{j=1}^N$. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3639 10.1512/iumj.2009.58.3639 en Indiana Univ. Math. J. 58 (2009) 1777 - 1796 state-of-the-art mathematics http://iumj.org/access/