Julia sets are uniformly perfect
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- by R. Mañé and L. F. da Rocha
- Proc. Amer. Math. Soc. 116 (1992), 251-257
- DOI: https://doi.org/10.1090/S0002-9939-1992-1106180-2
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Abstract:
We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets. As a corollary we give a very short proof of Lopes converse to Brolin’s theorem.References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 251-257
- MSC: Primary 58F23; Secondary 30D05, 31A25, 58F11
- DOI: https://doi.org/10.1090/S0002-9939-1992-1106180-2
- MathSciNet review: 1106180