Asymptotic perturbation of graph iterated function systems

Abstract

We study an asymptotic perturbation of the limit set generated from a finitely family of conformal contraction maps endowed with a directed graph. We show that if those maps have asymptotic expansions under weak conditions, then the Hausdorff dimension of the limit set behaves asymptotically by the same order. We also prove that the Gibbs measure of a suitable potential and the measure theoretic entropy of this measure have asymptotic expansions under an additional condition. In final section, we demonstrate degeneration of graph iterated function systems.