2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62350In 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.Dynamical Systems37F45, 37F30Remarks on Ruelle operator and Invariant Line Field Problemtext