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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bergweiler, Walter 2012. On the packing dimension of the Julia set and the escaping set of an entire function. Israel Journal of Mathematics, Vol. 192, Issue. 1, p. 449.

    Costin, O and Huang, M 2011. Geometric construction and analytic representation of Julia sets of polynomial maps. Nonlinearity, Vol. 24, Issue. 4, p. 1311.

    Rempe, Lasse Rippon, Philip J. and Stallard, Gwyneth M. 2010. Are Devaney hairs fast escaping?. Journal of Difference Equations and Applications, Vol. 16, Issue. 5-6, p. 739.

    BARAŃSKI, KRZYSZTOF 2008. Hausdorff dimension of hairs and ends for entire maps of finite order. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 145, Issue. 03, p. 719.

    Barański, Krzysztof and Karpińska, Bogusława 2007. Coding trees and boundaries of attracting basins for some entire maps. Nonlinearity, Vol. 20, Issue. 2, p. 391.

    Barański, Krzysztof 2007. Trees and hairs for some hyperbolic entire maps of finite order. Mathematische Zeitschrift, Vol. 257, Issue. 1, p. 33.

    Stallard, Gwyneth M. 1996. The Hausdorff dimension of Julia sets of entire functions II. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 119, Issue. 03, p. 513.

  • Ergodic Theory and Dynamical Systems, Volume 11, Issue 4
  • December 1991, pp. 769-777

The Hausdorff dimension of Julia sets of entire functions

  • Gwyneth M. Stallard (a1)
  • DOI:
  • Published online: 01 September 2008

We construct a set of transcendental entire functions such that the Hausdorff dimensions of the Julia sets of these functions have greatest lower bound equal to one.

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[2]H. Brolin . Invariant sets under iteration of rational functions. Arkiv Mat. 6 (1965), 103144.

[5]P. Fatou . Sur l'itération des fonctions transcendantes entières. Acta Math. 47 (1926), 337370.

[8]C. McMullen . Area and Hausdorff dimension of Julia sets of entire functions. Trans. Amer. Math. Soc. 300 (1987), 329342.

[9]G. Pólya & G. Szegö . Problems and Theorems in Analysis I (Part III, problems 158–160). Springer, New York, 1972.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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