%0 Journal Article %T Remarks on Ruelle operator and Invariant Line Field Problem %A Peter M. Makienko %J Mathematics %D 2001 %I arXiv %X In case of Lebesgue measure zero of postcritical set the necessary and sufficient conditions (in terms of convergence of sequences of measures) of existence of invariant conformal structures on J(R) are obtained. %U http://arxiv.org/abs/math/0110093v1