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THE HAUSDORFF DIMENSION OF JULIA SETS OF MEROMORPHIC FUNCTIONS II

  • GWYNETH M. STALLARD (a1)

Abstract

A family of transcendental meromorphic functions, fp(z), pN is considered. It is shown that, if p [ges ] 6, then the Hausdorff dimension of the Julia set of λfp satisfies dim Jfp) [les ] 1/p, for 0 < λ < 1/6p, and dim Jfp) [ges ] 1−(30 ln ln p/ln p), for p4p−1/105 ln p < λ < p4p−1/104 ln p. These results are used elsewhere to show that, for each d ∈ (0, 1), there exists a transcendental meromorphic function for which dim J(f) = d.

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THE HAUSDORFF DIMENSION OF JULIA SETS OF MEROMORPHIC FUNCTIONS II

  • GWYNETH M. STALLARD (a1)

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