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Abstract: We show that if the maximum modulus of a quasiregular mapping f growssufficiently rapidly then there exists a non-empty escaping set If consistingof points whose forward orbits under iteration tend to infinity. This set Ifhas an unbounded component but, in contrast to the case of entire functions onthe complex plane, the closure of If may have a bounded component.



Author: Walter Bergweiler, Alastair Fletcher, Jim Langley, Janis Meyer

Source: https://arxiv.org/



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