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The iterated minimum modulus and conjectures of Baker and Eremenko

  • John W. Osborne
  • Philip J. RipponEmail author
  • Gwyneth M. Stallard
Article
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Abstract

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the minimum modulus, and obtain new results related to Eremenko’s conjecture and Baker’s conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function.

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • John W. Osborne
    • 1
  • Philip J. Rippon
    • 1
    Email author
  • Gwyneth M. Stallard
    • 1
  1. 1.School of Mathematics and StatisticsThe Open UniversityMilton KeynesUK

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