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 language | English |
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Pages (from-to) | 119-132 |
Number of pages | 14 |
Journal | Communications in Mathematical Physics |
Volume | 141 |
Issue number | 1 |
DOIs | |
State | Published - Oct 1991 |