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Orthogonality and the Hausdorff dimension of the maximal measure


Author: Artur Oscar Lopes
Journal: Proc. Amer. Math. Soc. 98 (1986), 51-55
MSC: Primary 58F11; Secondary 30D05, 42C05, 58F08
DOI: https://doi.org/10.1090/S0002-9939-1986-0848874-7
MathSciNet review: 848874
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Abstract: In this paper the orthogonality properties of iterated polynomials are shown to remain valid in some cases for rational maps. Using a functional equation fulfilled by the generating function, the author shows that the Hausdorff dimension of the maximal measure is a real analytical function of the coefficients of an Axiom A rational map satisfying the property that all poles of $ f$ and zeros of $ f'(z)$ have multiplicity one.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0848874-7
Keywords: Hausdorff dimension, rational maps, orthogonality, Axiom A, generating function
Article copyright: © Copyright 1986 American Mathematical Society

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