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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Families of Baker domains II
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by P. J. Rippon and G. M. Stallard PDF
Conform. Geom. Dyn. 3 (1999), 67-78 Request permission

Abstract:

Let $f$ be a transcendental meromorphic function and $U$ be an invariant Baker domain of $f$. We use estimates for the hyperbolic metric to show that there is a relationship between the size of $U$ and the proximity of $f$ in $U$ to the identity function, and illustrate this by discussing how the dynamics of transcendental entire functions of the following form vary with the parameter $a$: \begin{equation*} f(z) = az + bz^ke^{-z}(1+o(1)) \; \text { as } \Re (z) \rightarrow \infty , \end{equation*} where $k \in \mathbf N$, $a \geq 1$ and $b > 0$.
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Additional Information
  • P. J. Rippon
  • Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA England
  • MR Author ID: 190595
  • Email: p.j.rippon@open.ac.uk
  • G. M. Stallard
  • Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA England
  • MR Author ID: 292621
  • Email: g.m.stallard@open.ac.uk
  • Received by editor(s): January 5, 1999
  • Received by editor(s) in revised form: April 19, 1999
  • Published electronically: June 14, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 3 (1999), 67-78
  • MSC (1991): Primary 30D05; Secondary 58F08
  • DOI: https://doi.org/10.1090/S1088-4173-99-00045-4
  • MathSciNet review: 1689255