On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points II

Abstract

Following the attracting and preperiodic cases ([FJT]), in this paper we prove the existence of weakly repelling fixed points for transcendental meromorphic maps, provided that their Fatou set contains a multiply connected parabolic basin. We use quasi-conformal surgery and virtually repelling fixed point techniques. © Instytut Matematyczny PAN, 2011.