English

Slow escape in tracts

Dynamical Systems 2018-09-05 v1 Complex Variables

Abstract

Let ff be a transcendental entire function. By a result of Rippon and Stallard, there exist points whose orbit escapes arbitrarily slowly. By using a range of techniques to prove new covering results, we extend their theorem to prove the existence of points which escape arbitrarily slowly within logarithmic tracts and tracts with certain boundary properties. We then give examples to illustrate our results in a variety of tracts.

Keywords

Cite

@article{arxiv.1809.01068,
  title  = {Slow escape in tracts},
  author = {James Waterman},
  journal= {arXiv preprint arXiv:1809.01068},
  year   = {2018}
}

Comments

15 pages

R2 v1 2026-06-23T03:53:58.293Z