Zeta functions and transfer operators for piecewise monotone transformations |
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| Authors: | V Baladi G Keller |
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| Institution: | (1) Section de Mathématiques, Université de Genève, CH-1211 Geneva 24, Switzerland;(2) Institut für Angewandte Mathematik und SFB 123, Universität Heidelberg, D-6900 Heidelberg 1, Federal Republic of Germany;(3) Present address: Mathematisches Institut, Universität Erlangen-Nürnberg, D-8520 Erlangen, FRG |
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| Abstract: | Given a piecewise monotone transformationT of the interval and a piecewise continuous complex weight functiong of bounded variation, we prove that the Ruelle zeta function  (z) of (T, g) extends meromorphically to { z< -1} (where =lim  g°Tn-1...g°Tg
1/n
) and thatz is a pole of if and only ifz
–1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant.Research partially supported by the Fonds National Suisse |
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