Orthogonality and the hausdorff dimension of the maximal measure

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 co...

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Detalles Bibliográficos
Autor: Lopes, Artur Oscar
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1986
País:Brasil
Institución:Universidade Federal do Rio Grande do Sul (UFRGS)
Repositorio:Repositório Institucional da UFRGS
Idioma:inglés
OAI Identifier:oai:www.lume.ufrgs.br:10183/27485
Acceso en línea:http://hdl.handle.net/10183/27485
Access Level:acceso abierto
Palabra clave:Ortogonalidade : Medida maxima : Dimensao de hausdorff
Descripción
Sumario: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 ƒ and zeros of ƒ’(z) have multiplicity one.