Exotic baker and wandering domains for Ahlfors islands maps |
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| Authors: | Lasse Rempe Philip J Rippon |
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| Institution: | 1.Department of Mathematical Sciences,University of Liverpool,Liverpool,UK;2.Department of Mathematics and Statistics,The Open University Walton Hall,Milton Keynes,UK |
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| Abstract: | Let X be a compact Riemann surface of genus at most 1, i.e., the Riemann sphere or a torus, and let W ⊊ X be an arbitrary domain. We construct a variety of examples of holomorphic functions g: W → X that satisfy Epstein’s Ahlfors islands property and that have “pathological” dynamical behaviour. In particular, we show that the accumulation set of any curve tending to the boundary of W can be realized as the ω-limit set of a Baker domain of such a function. We furthermore construct Ahlfors islands maps | • | with wandering domains having prescribed ω-limit sets |
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