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 | References | Similar Articles | Additional Information

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 and zeros of 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