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 ζ(z) of (T, g) extends meromorphically to {∣z∣<θ-1} (where θ=lim ∥g°Tn-1...g°Tg∥ 1/n∞ ) and thatz is a pole of ζ 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.
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Communicated by J.-P. Eckmann
Research partially supported by the Fonds National Suisse
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Baladi, V., Keller, G. Zeta functions and transfer operators for piecewise monotone transformations. Commun.Math. Phys. 127, 459–477 (1990). https://doi.org/10.1007/BF02104498
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DOI: https://doi.org/10.1007/BF02104498