Ruelle Operator for Infinite Conformal Ifs
نویسندگان
چکیده
Let (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) be a contractive iterated function system (IFS), where X is a compact subset of R. It is well known that there exists a unique nonempty compact set K such that K = ⋃m j=1 wj(K). Moreover, the Ruelle operator on C(K) determined by the IFS (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) has been introduced in [FL]. In the present paper, the Ruelle operators determined by the infinite conformal IFSs are discussed. Some separation properties for the infinite conformal IFSs are investigated by using the Ruelle operator.
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