English

The escaping set of a quasiregular mapping

Complex Variables 2009-01-17 v1

Abstract

We show that if the maximum modulus of a quasiregular mapping f grows sufficiently rapidly then there exists a non-empty escaping set I(f) consisting of points whose forward orbits under iteration tend to infinity. This set I(f) has an unbounded component but, in contrast to the case of entire functions on the complex plane, the closure of I(f) may have a bounded component.

Keywords

Cite

@article{arxiv.0802.0119,
  title  = {The escaping set of a quasiregular mapping},
  author = {Walter Bergweiler and Alastair Fletcher and Jim Langley and Janis Meyer},
  journal= {arXiv preprint arXiv:0802.0119},
  year   = {2009}
}

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10 pages