## Zeta functions and transfer operators for piecewise monotone transformations.(English)Zbl 0703.58048

Given a piecewise monotone transformation T of the interval and a piecewise continuous complex weight function g of bounded variation, the authors prove that the Ruelle zeta function $$\zeta$$ (z) of (T,g) extends meromorphically to $$\{| z| <\theta^{-1}\}$$ (where $$\theta =\lim_{n\to \infty}\| g\circ T^{n-1}\cdot...\cdot g\circ T\cdot g\|_{\infty}^{1/n})$$ and that z is a pole of $$\zeta$$ if and only if $$z^{-1}$$ is an eigenvalue of the corresponding transfer operator $${\mathcal L}$$. They do not assume that $${\mathcal L}$$ leaves a reference measure invariant.
Reviewer: G.M.Rassias

### MSC:

 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 37C80 Symmetries, equivariant dynamical systems (MSC2010) 30D50 Blaschke products, etc. (MSC2000)
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### References:

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