Ruelle operators with rational weights for Julia sets

G. Levin, M. Sodin, P. Yuditskii

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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.

Original languageEnglish
Pages (from-to)303-331
Number of pages29
JournalJournal d'Analyse Mathematique
Volume63
Issue number1
DOIs
StatePublished - Dec 1994
Externally publishedYes

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