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The Hausdorff dimension of Julia sets of entire functions

  • Gwyneth M. Stallard (a1)

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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