A Ruelle operator for a real Julia set

G. M. Levin*, M. L. Sodin, P. M. Yuditski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let R be an expanding rational function with a real bounded Julia set, and let {Mathematical expression} be a Ruelle operator acting in a space of functions analytic in a neighbourhood of the Julia set. We obtain explicit expressions for the resolvent function {Mathematical expression} and, in particular, for the Fredholm determinant D(λ)=det(I-λL). It gives us an equation for calculating the escape rate. We relate our results to orthogonal polynomials with respect to the balanced measure of R. Two examples are considered.

Original languageEnglish
Pages (from-to)119-132
Number of pages14
JournalCommunications in Mathematical Physics
Volume141
Issue number1
DOIs
StatePublished - Oct 1991
Externally publishedYes

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