Area and Hausdorff dimension of Julia sets of entire functions

McMullen, Curt

doi:10.1090/S0002-9947-1987-0871679-3

Area and Hausdorff dimension of Julia sets of entire functions
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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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