Zeta functions and transfer operators for piecewise monotone transformations - Baladi, Viviane; Keller, Gerhard (Communications in Mathematical Physics, 1990)
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.