The growth rate of an entire function and the Hausdorff dimension of its Julia set

• Autores: Walter Bergweiler, Boguslawa Karpinska, Gwyneth M. Stallard
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 3, 2009, págs. 680-698
• Idioma: inglés
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• Resumen

  • Let f be a transcendental entire function in the Eremenko�Lyubich class B. We give a lower bound for the Hausdorff dimension of the Julia set of f that depends on the growth of f. This estimate is best possible and is obtained by proving a more general result concerning the size of the escaping set of a function with a logarithmic tract.