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  • Cited by 4
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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 and Peter, Jörn 2013. Escape rate and Hausdorff measure for entire functions. Mathematische Zeitschrift, Vol. 274, Issue. 1-2, p. 551.


    Aspenberg, Magnus and Bergweiler, Walter 2012. Entire functions with Julia sets of positive measure. Mathematische Annalen, Vol. 352, Issue. 1, p. 27.


    Zheng, Jian-Hua 2002. On transcendental meromorphic functions which are geometrically finite. Journal of the Australian Mathematical Society, Vol. 72, Issue. 01, p. 93.


    Bergweiler, Walter 1995. Invariant domains and singularities. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 117, Issue. 03, p. 525.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 108, Issue 3
  • November 1990, pp. 551-557

Entire functions with Julia sets of zero measure

  • Gwyneth M. Stallard (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100069437
  • Published online: 24 October 2008
Abstract
Abstract

We extend results of McMullen about the dynamics of entire functions for which the orbits of the critical values stay away from the Julia set. In particular we show that such functions are expanding on their Julia sets which have self-similarity properties. Under suitable further conditions the Julia sets have plane measure zero.

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

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

[8]D. Sullivan . Conformal dynamical systems. In Geometric Dynamics, Lecture Notes in Math. vol. 1007 (Springer-Verlag, 1983), pp. 725752.

[9]D. Sullivan . Quasiconformal homeomorphisms and dynamics 1. Ann. of Math. (2) 122 (1985), 401418.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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