| Abstract: |
| We study a perturbed graph-directed iterated function system (GIFS) that some perturbed contraction maps converge to constant values. In our situation, the perturbed GIFS has a unique Gibbs measure $\mu(\epsilon,\cdot)$ associated with the dimension of the limit set for each $\epsilon>0$ and on the other hand the unperturbed GIFS possesses several Gibbs measures $\mu_{1},\mu_{2},\dots, \mu_{m}$. In particular, any limit point of $\mu(\epsilon,\cdot)$ in the sense of weak topology is expressed as a convex combination of $\mu_{1},\mu_{2},\dots, \mu_{m}$. In this talk, under suitable conditions, we give a necessary and sufficient condition for convergence of $\mu(\epsilon,\cdot)$ using solutions of Bowen`s equations and measure-theoretic entropies of Gibbs measures. |
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