Ruelle operator for infinite conformal iterated function systems

Let (X; {w(j)}(j-1)(m) {P-j}(j=1)(m)) (2 <= m < infinity) be a contractive iterated function system (IFS), where Xis a compact subset of R-d. It is well known that there exists a unique nonempty compact set K such that K = U(j=1)(m)w(j)(K). Moreover, the Ruelle operator on C(K) determined by the IFS (X; {w(j))(j-1;)(m) {Pj}(j-1)(m)) (2 <= m < infinity) has been extensively studied. 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. (c) 2012 Elsevier Ltd. All rights reserved.