Topological and Combinatorial Problems in One-dimensional Complex Dynamics
timetable:
Thu 17 Oct, 16:45 - 17:15, Aula Dini
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Connectivity of Baker domains of meromorphic functions
speaker: Núria Fagella (Universitat de Barcelona)abstract: We conclude the proof that every transcendental meromorphic map f with a disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions whose iterates tend to a boundary point. In particular, the results answer the open question of whether periodic Baker domains of Newton's method for entire maps are simply connected.
timetable:
Thu 17 Oct, 16:45 - 17:15, Aula Dini
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