Zeta functions and transfer operators for piecewise monotone transformations

Baladi V, Keller G (1990)

Publication Type: Journal article, Original article

Publication year: 1990

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 127

Pages Range: 459--477

Journal Issue: 3

URI: http://projecteuclid.org/euclid.cmp/1104180216

DOI: 10.1007/BF02104498

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^°T^n-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.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

University of Geneva / Université de Genève (UNIGE)

Switzerland (CH)

How to cite

APA:

Baladi, V., & Keller, G. (1990). Zeta functions and transfer operators for piecewise monotone transformations. Communications in Mathematical Physics, 127(3), 459--477. https://doi.org/10.1007/BF02104498

MLA:

Baladi, Viviane, and Gerhard Keller. "Zeta functions and transfer operators for piecewise monotone transformations." Communications in Mathematical Physics 127.3 (1990): 459--477.

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