Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps

Buzzi J, Keller G (2001)

Publication Type: Journal article, Original article

Publication year: 2001

Journal

Ergodic Theory and Dynamical Systems Cambridge University Press (CUP)

Publisher: Cambridge University Press (CUP)

Book Volume: 21

Pages Range: 690-716

DOI: 10.1017/S0143385701001341

Abstract

Let X ⊂ ℝ2 be a finite union of bounded polytopes and let T : X → X be piecewise affine and eventually expanding. Then the Perron-Frobenius operator £ of T is quasicompact as an operator on the space of functions of bounded variation on ℝ2 and its isolated eigenvalues (including multiplicities) are just the reciprocals of the poles of the dynamical zeta function of T. In higher dimensions the result remains true under an additional generically satisfied transversality assumption.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

University of Paris 11 - Paris-Sud / Université Paris XI Paris-Sud FR France (FR)

How to cite

APA:

Buzzi, J., & Keller, G. (2001). Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps. Ergodic Theory and Dynamical Systems, 21, 690-716. https://dx.doi.org/10.1017/S0143385701001341

MLA:

Buzzi, Jérôme, and Gerhard Keller. "Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps." Ergodic Theory and Dynamical Systems 21 (2001): 690-716.

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