The local connectivity of the boundary of a simply connected Fatou component U allows us to understand the dynamics on the closure of U. For transcendental entire maps an unbounded non-univalent Fatou component can never have a locally connected boundary. In this talk we prove local connectivity of boundaries of invariant simply connected attracting basins for a class of transcendental meromorphic maps. These basin boundaries, which may be unbounded, can contain singular values as well as the essential singularity at infinity but we assume that their unbounded parts are contained in regions where the map exhibits a kind of 'parabolic' behavior.

The talk is based on a joint work with Krzysztof Barański, Nuria Fagella and Xavier Jarque.

Meeting ID: 852 4277 3200 Passcode: 103121