Ruelle operators with rational weights for Julia sets

G. Levin; M. Sodin; P. Yuditskii

doi:10.1007/BF03008428

Ruelle operators with rational weights for Julia sets

G. Levin^*, M. Sodin, P. Yuditskii

^*Corresponding author for this work

Einstein Institute of Mathematics

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Abstract

Let R be a rational function with nonempty set of normality that consists of basins of attraction only and let {Mathematical expression} be a Ruelle operator with a rational weight Q which acts in a space of locally analytic functions on the Julia set of R. We obtain explicit expressions for equations for the eigenvalues and study the structure of eigenfunctions of L_Q and its adjoint operator. Some applications to operators important for measurable dynamics of rational functions will be considered.

Original language	English
Pages (from-to)	303-331
Number of pages	29
Journal	Journal d'Analyse Mathematique
Volume	63
Issue number	1
DOIs	https://doi.org/10.1007/BF03008428
State	Published - Dec 1994

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abstract = "Let R be a rational function with nonempty set of normality that consists of basins of attraction only and let {Mathematical expression} be a Ruelle operator with a rational weight Q which acts in a space of locally analytic functions on the Julia set of R. We obtain explicit expressions for equations for the eigenvalues and study the structure of eigenfunctions of LQ and its adjoint operator. Some applications to operators important for measurable dynamics of rational functions will be considered.",

author = "G. Levin and M. Sodin and P. Yuditskii",

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AB - Let R be a rational function with nonempty set of normality that consists of basins of attraction only and let {Mathematical expression} be a Ruelle operator with a rational weight Q which acts in a space of locally analytic functions on the Julia set of R. We obtain explicit expressions for equations for the eigenvalues and study the structure of eigenfunctions of LQ and its adjoint operator. Some applications to operators important for measurable dynamics of rational functions will be considered.

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Ruelle operators with rational weights for Julia sets

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