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}
}
Comments
10 pages