Ruelle operators with rational weights for Julia sets

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageAmerican English
Pages (from-to)303-331
Number of pages29
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Dec 1994


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