# Ruelle Operator for Infinite Conformal IFS - Mathematics > Dynamical Systems

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Abstract: Let $X, \{w j \} {j=1}^m, \{p j \} {j=1}^m$ $2 \leq m < \infty$ be acontractive iterated function system IFS, where $X$ is a compact subset of${\Bbb{R}}^d$. It is well known that there exists a unique nonempty compact set$K$ such that $K=\bigcup {j=1}^m w jK$. Moreover, the Ruelle operator on$CK$ determined by the IFS $X, \{w j \} {j=1}^m, \{p j \} {j=1}^m$ $2 \leqm < \infty$ has been introduced in \cite{FL}. In the present paper, the Ruelleoperators determined by the infinite conformal IFSs are discussed. Someseparation properties for the infinite conformal IFSs are investigated by usingthe Ruelle operator.

Author: ** Xiao-Peng Chen, Li-Yan Wu, Yuan-Ling Ye**

Source: https://arxiv.org/