A Ruelle operator for a real Julia set期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A Ruelle operator for a real Julia set

Authors:	G. M. Levin M. L. Sodin P. M. Yuditski

Affiliation:	(1) Institute of Mathematics, Hebrew University of Jerusalem, 91904, Israel;(2) Mathematical Division of the Institute for Low Temperature Physics and Engineering, Lenin Av. 47, 310164 Kharkov, USSR;(3) Institute for Mechanization and Electrification of Agriculture, Kharkov, USSR

Abstract:	LetR be an expanding rational function with a real bounded Julia set, and let $left( {Lg} right)left( x right) = sumlimits_{Ry = x} {frac{{gleft( y right)}}{{left[ {R'left( y right)} right]^2 }}}$ 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 $Eleft( {x,z;lambda } right) = left( {I - lambda L} right)^{ - 1} frac{1}{{z - x}}$ and, in particular, for the Fredholm determinantD()=det(I-L). It gives us an equation for calculating the escape rate. We relate our results to orthogonal polynomials with respect to the balanced measure ofR. Two examples are considered.The first named author was sponsored in part by the Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation (Germany)

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