Slow escaping points of meromorphic functions

  title={Slow escaping points of meromorphic functions},
  author={Philip Jonathan Rippon and Gwyneth M. Stallard},
We show that for any transcendental meromorphic function f there is a point z in the Julia set of f such that the iterates fn(z) escape, that is, tend to ∞, arbitrarily slowly. The proof uses new covering results for analytic functions. We also introduce several slow escaping sets, in each of which fn(z) tends to ∞ at a bounded rate, and establish the connections between these sets and the Julia set of f . To do this, we show that the iterates of f satisfy a strong distortion estimate in all… CONTINUE READING

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