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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Area and Hausdorff dimension of Julia sets of entire functions
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by Curt McMullen PDF
Trans. Amer. Math. Soc. 300 (1987), 329-342 Request permission

Abstract:

We show the Julia set of $\lambda \sin (z)$ has positive area and the action of $\lambda \sin (z)$ on its Julia set is not ergodic; the Julia set of $\lambda \exp (z)$ has Hausdorff dimension two but in the presence of an attracting periodic cycle its area is zero.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 300 (1987), 329-342
  • MSC: Primary 30D05; Secondary 58F08, 58F20
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0871679-3
  • MathSciNet review: 871679